source stringclasses 9
values | usr stringlengths 10 6.1k | cot stringlengths 106 54.3k | bot stringlengths 9 18.4k ⌀ |
|---|---|---|---|
orca_math | There were 27 boys and 35 girls on the playground at recess. There were _____ children on the playground at recess. | First, I need to determine the total number of children on the playground by adding the number of boys and girls.
There are 27 boys and 35 girls.
Adding these together: 27 boys + 35 girls = 62 children.
Therefore, the total number of children on the playground is 62. | To find the total number of children on the playground, we simply add the number of boys and girls together.
\[
\text{Total children} = \text{Number of boys} + \text{Number of girls}
\]
Plugging in the given values:
\[
\text{Total children} = 27 \text{ boys} + 35 \text{ girls} = 62 \text{ children}
\]
**Final Answe... |
synthetic_math | John purchased three dozen oranges for $\$$28.80. At the same rate, how much would five dozen of these oranges cost? | First, I need to determine the cost per dozen oranges. John bought three dozen oranges for \$28.80, so I can find the cost per dozen by dividing the total cost by the number of dozens.
Next, with the cost per dozen known, I can calculate the cost for five dozen oranges by multiplying the cost per dozen by five.
Final... | **Solution:**
To determine the cost of five dozen oranges at the same rate, follow these steps:
1. **Find the cost per dozen:**
John purchased three dozen oranges for \$28.80. To find the cost per dozen, divide the total cost by the number of dozens.
\[
\text{Cost per dozen} = \frac{\$28.80}{3} = \$9.60 \t... |
orca_math | Bianca earned 5 points for each bag of cans she recycled. If she had 17 bags, but didn't recycle 8 of them, how many points would she have earned? | First, determine how many bags Bianca actually recycled by subtracting the number of bags she did not recycle from the total number of bags she had.
Then, calculate the total points she earned by multiplying the number of recycled bags by the points earned per bag. | **Solution:**
1. **Determine the number of bags Bianca recycled:**
Bianca had a total of 17 bags but did not recycle 8 of them. Therefore, the number of bags she actually recycled is:
\[
17 \text{ bags} - 8 \text{ bags} = 9 \text{ bags}
\]
2. **Calculate the total points earned:**
Bianca earns 5 ... |
orca_math | Each bottle cap costs $2. How much do 6 bottle caps cost? | First, identify the cost of one bottle cap, which is $2.
Next, determine the number of bottle caps needed, which is 6.
Multiply the cost per bottle cap by the number of bottle caps: 6 × $2 = $12.
Therefore, the total cost for 6 bottle caps is $12. | To determine the total cost of 6 bottle caps, follow these easy steps:
1. **Identify the cost per bottle cap:**
Each bottle cap costs \$2.
2. **Determine the number of bottle caps:**
You need 6 bottle caps.
3. **Calculate the total cost:**
\[
\text{Total Cost} = \text{Number of Bottle Caps} \... |
orca_math | Jack received 6 emails in the morning and some emails in the afternoon. He received 2 more emails in the afternoon than in the morning. How many emails did Jack receive in the afternoon? | First, I need to determine how many emails Jack received in the afternoon.
I know that Jack received 6 emails in the morning.
It is also given that he received 2 more emails in the afternoon than in the morning.
To find the total number of emails received in the afternoon, I will add the number of emails received in... | **Solution:**
Let's determine how many emails Jack received in the afternoon.
1. **Emails in the Morning:**
Jack received **6 emails** in the morning.
2. **Additional Emails in the Afternoon:**
He received **2 more emails** in the afternoon than in the morning.
3. **Calculating Afternoon Emails:**
... |
orca_math | Leif’s apple tree has 14 apples and his orange tree has 2 dozen oranges. How many more oranges does he have than apples? | First, I need to determine the number of apples and oranges Leif has.
Leif has 14 apples.
He also has 2 dozen oranges. Since 1 dozen equals 12, 2 dozen equals 24 oranges.
To find out how many more oranges he has than apples, I subtract the number of apples from the number of oranges.
24 oranges minus 14 apples equa... | **Solution:**
1. **Determine the number of apples:**
\[
\text{Number of apples} = 14
\]
2. **Determine the number of oranges:**
\[
\text{Number of oranges} = 2 \text{ dozen} = 2 \times 12 = 24
\]
3. **Calculate how many more oranges there are than apples:**
\[
\text{Difference} = \text{Number... |
cn_k12 | Compare the sizes: $\pi$ ____ $3.14$ (fill in the blank with $=$, $>$, or $<$). | First, I recognize that π is a well-known mathematical constant approximately equal to 3.141592653589793.
Next, I compare this value to 3.14. By examining the decimal places, I see that 3.141592653589793 is greater than 3.14.
Therefore, I conclude that π is greater than 3.14. | To compare the sizes of \(\pi\) and \(3.14\), let's analyze their approximate values.
1. **Approximate Value of \(\pi\):**
\[
\pi \approx 3.141592653589793
\]
2. **Compare with \(3.14\):**
\[
3.141592653589793 > 3.14
\]
3. **Conclusion:**
\[
\pi > 3.14
\]
**Final Answer:**
\[
\boxed{>}
\] |
orca_math | Find the value of adding 3 to the number of diagonals in the rectangle. | First, I need to determine the number of diagonals in a rectangle. A rectangle has four sides, and each vertex connects to two non-adjacent vertices, resulting in two diagonals.
Next, I will add 3 to the number of diagonals. So, 2 diagonals plus 3 equals 5.
Therefore, the final value after adding 3 to the number of d... | To find the value of adding 3 to the number of diagonals in a rectangle, follow these steps:
1. **Determine the Number of Diagonals in a Rectangle:**
A rectangle has **4 sides**. The formula to calculate the number of diagonals in a polygon with \( n \) sides is:
\[
\frac{n(n - 3)}{2}
\]
Plu... |
orca_math | The zoo keeps 35 female (a) animals. Males outnumber females by 7. How many (a) animals are there in all? | First, I need to determine the number of male animals. Since males outnumber females by 7, I can calculate the number of males by adding 7 to the number of females.
Next, I will add the number of female animals to the number of male animals to find the total number of animals in the zoo. | **Solution:**
We are given:
- Number of female animals (\( F \)) = 35
- Males outnumber females by 7
Let's denote:
- Number of male animals as \( M \)
**Step 1:** Determine the number of male animals.
Since males outnumber females by 7:
\[
M = F + 7 = 35 + 7 = 42
\]
**Step 2:** Calculate the total number of animal... |
orca_math | Jessica has 3 dozen red marbles. Sandy has 4 times more red marbles than Jessica. How many red marbles does Sandy have? | First, determine the number of red marbles Jessica has by calculating 3 dozen, which equals 3 multiplied by 12.
Next, calculate how many times more red marbles Sandy has compared to Jessica by multiplying Jessica's total by 4.
Finally, present the result as the total number of red marbles Sandy has. | **Solution:**
1. **Determine the number of red marbles Jessica has:**
Jessica has **3 dozen** red marbles. Since one dozen equals 12 marbles:
\[
3 \text{ dozen} = 3 \times 12 = 36 \text{ marbles}
\]
2. **Calculate how many red marbles Sandy has:**
Sandy has **4 times more** red marbles than Jessi... |
synthetic_math | Marguerite drove 150 miles in 3 hours. If Sam drove for 4.5 hours at the same average rate as Marguerite, how many miles did he drive? | First, I need to determine Marguerite's average speed by dividing the distance she drove by the time she took.
Next, I'll use this average speed to calculate how many miles Sam drove by multiplying the speed by the time he spent driving.
Finally, I'll present the calculated distance that Sam drove. | **Solution:**
1. **Calculate Marguerite's average speed:**
Marguerite drove 150 miles in 3 hours. To find her average speed:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ mph}
\]
2. **Determine the distance Sam drove:**
Sam drove for 4.5... |
orca_math | The Sumata family took a vacation by car. Each day they drove 250 miles. They drove 1250 miles in total. How many days did their vacation last? | First, I need to determine how many days the Sumata family spent on their vacation. They drove a total of 1250 miles and covered 250 miles each day.
To find the number of days, I will divide the total miles driven by the miles driven each day.
So, 1250 miles divided by 250 miles per day equals 5 days.
Therefore, the... | **Solution:**
To determine how many days the Sumata family's vacation lasted, we can use the following steps:
1. **Identify the total miles driven:**
\[
\text{Total miles} = 1250 \text{ miles}
\]
2. **Identify the miles driven each day:**
\[
\text{Miles per day} = 250 \text{ miles/day}
\]
3. *... |
orca_math | Eugene has 51.0 pencils. He gives some pencils to Joyce and has 45 pencils left. How many pencils did Eugene give to Joyce? | First, I note that Eugene initially has 51.0 pencils.
After giving some pencils to Joyce, Eugene has 45 pencils remaining.
To find out how many pencils Eugene gave to Joyce, I subtract the number of pencils he has left from the initial number of pencils he had.
So, 51.0 pencils minus 45 pencils equals 6 pencils.
Th... | **Solution:**
Eugene initially has **51.0 pencils**. After giving some pencils to Joyce, he is left with **45 pencils**. To find out how many pencils Eugene gave to Joyce, we can use the following steps:
1. **Initial Number of Pencils:**
\[
51.0 \text{ pencils}
\]
2. **Number of Pencils Left:**
\[
45 ... |
orca_math | 2 birds and 6 storks were sitting on the fence. 3 more birds came to join them. How many more storks than birds are sitting on the fence? | First, I note that there are initially 2 birds and 6 storks on the fence.
Then, 3 more birds join them, increasing the total number of birds to 2 + 3 = 5 birds.
To find out how many more storks there are compared to birds, I subtract the number of birds from the number of storks: 6 storks - 5 birds = 1 more stork tha... | **Solution:**
Let's break down the problem step by step.
1. **Initial Count:**
- **Birds:** 2
- **Storks:** 6
2. **Additional Birds Join:**
- **Birds Added:** 3
- **Total Birds Now:** \( 2 + 3 = 5 \)
3. **Comparing Storks and Birds:**
- **Number of Storks:** 6
- **Number of Birds:** 5
- **Diffe... |
orca_math | For Halloween, Sarah received 66 pieces of candy from neighbors and 15 pieces from her older sister. She ate a certain number of pieces a day, and the candy lasted her 9 days. How many pieces of candy did she eat per day? | First, I need to determine the total number of pieces of candy Sarah received. She got 66 pieces from her neighbors and 15 pieces from her older sister.
Next, I'll add these two amounts together to find the total number of candies:
66 (from neighbors) + 15 (from sister) = 81 pieces of candy
Sarah ate these candies o... | **Solution:**
To determine how many pieces of candy Sarah ate each day, follow these steps:
1. **Calculate the total number of candies Sarah received:**
\[
\text{Candies from neighbors} + \text{Candies from sister} = 66 + 15 = 81 \text{ pieces}
\]
2. **Determine how many pieces Sarah ate each day:**
\[... |
orca_math | Tom had 27 pennies and 15 dimes in his bank. His dad gave him 33 dimes and 49 nickels. How many dimes does he have now? | First, I identify the number of dimes Tom initially has, which is 15.
Next, I note that his dad gave him an additional 33 dimes.
To find the total number of dimes Tom has now, I add the original number of dimes to the number of dimes his dad gave him.
So, 15 (original dimes) plus 33 (additional dimes) equals 48 dime... | **Solution:**
To determine how many dimes Tom has now, follow these steps:
1. **Initial Dimes:**
- Tom originally has **15 dimes**.
2. **Dimes Given by Dad:**
- His dad gave him **33 dimes**.
3. **Total Dimes Now:**
- Add the initial dimes to the dimes given by his dad:
\[
15 \text{ dimes} + 33 \... |
orca_math | Big boxes contain 7 dolls each. Small boxes contain 4 dolls each. There are 5 big boxes and 9 small boxes. How many dolls are there in total? | First, determine the number of dolls in the big boxes by multiplying the number of big boxes by the number of dolls each big box contains.
Next, determine the number of dolls in the small boxes by multiplying the number of small boxes by the number of dolls each small box contains.
Finally, add the number of dolls fr... | To find the total number of dolls, follow these steps:
1. **Calculate the number of dolls in the big boxes:**
\[
\text{Number of big boxes} \times \text{Dolls per big box} = 5 \times 7 = 35 \text{ dolls}
\]
2. **Calculate the number of dolls in the small boxes:**
\[
\text{Number of small boxes}... |
cn_k12 | Put 6 kg of salt into 30 kg of water. The weight of the salt accounts for what fraction of the total weight of the saltwater solution?
A: $\boxed{\frac{1}{5}}$
B: $\boxed{\frac{1}{6}}$
C: $\boxed{\frac{1}{30}}$
D: | First, I need to determine the total weight of the saltwater solution by adding the weight of the salt to the weight of the water.
Next, I will calculate the fraction of the total weight that the salt represents by dividing the weight of the salt by the total weight of the solution.
Finally, I will simplify the fract... | **Solution:**
We are asked to find the fraction of the total weight of the saltwater solution that is accounted for by the salt.
1. **Determine the total weight of the saltwater solution:**
\[
\text{Total weight} = \text{Weight of salt} + \text{Weight of water} = 6\, \text{kg} + 30\, \text{kg} = 36\, \text{kg}... |
synthetic_amc | In a geometric configuration, angle $C$ measures $120^\circ$ and forms a linear pair with angle $D$. In an adjacent triangle, angle $E$ measures $50^\circ$ and angle $F$ is congruent to angle $D$. Determine the measure of angle $G$, the third angle in the triangle containing angles $E$ and $F$.
$\text{(A)}\ 50^\circ \q... | To determine the measure of angle \( G \), we start by noting that angle \( C \) is \( 120^\circ \) and forms a linear pair with angle \( D \). Since linear pairs add up to \( 180^\circ \), we can find angle \( D \) as follows:
\[
D = 180^\circ - 120^\circ = 60^\circ
\]
Next, we consider the triangle containing angle... | null |
orca_math | There are 10 balls. Jungkook wants to put 5 balls in one box. How many boxes does he need at this time? | First, I need to determine how many boxes Jungkook requires to store all 10 balls, with each box holding 5 balls.
To find the number of boxes, I can divide the total number of balls by the number of balls each box can hold.
So, 10 balls divided by 5 balls per box equals 2 boxes.
Therefore, Jungkook needs 2 boxes to ... | **Solution:**
Jungkook has a total of 10 balls and wants to place 5 balls in each box. To find out how many boxes he needs, follow these steps:
1. **Determine the total number of balls:**
Jungkook has **10 balls**.
2. **Determine the number of balls per box:**
Each box can hold **5 balls**.
3. **Calculate... |
orca_math | In a 60-item exam, Liza got 90% of the items correctly. Her best friend, Rose, got 2 more correct answers than her. How many incorrect answers did Rose have? | First, calculate the number of correct answers Liza got by finding 90% of 60.
Next, determine Rose's correct answers by adding 2 to Liza's correct answers.
Finally, subtract the number of correct answers Rose got from the total number of items to find the number of incorrect answers. | **Solution:**
1. **Calculate Liza's Correct Answers:**
Liza got 90% of the 60 items correct.
\[
\text{Correct Answers (Liza)} = 0.90 \times 60 = 54
\]
2. **Determine Rose's Correct Answers:**
Rose got 2 more correct answers than Liza.
\[
\text{Correct Answers (Rose)} = 54 + 2 = 56
\]... |
orca_math | Maria's birthday is in 22 days. Her friend Lilly wants to buy her flowers so she saves $2 each day until Maria's birthday. If a flower costs $4, how many flowers can Lilly buy? | First, I need to determine how much money Lilly saves in total. She saves $2 each day for 22 days.
Next, I calculate the total savings by multiplying the daily savings by the number of days:
$2/day * 22 days = $44.
Then, I find out how many flowers Lilly can buy by dividing the total savings by the cost per flower:
$... | **Solution:**
1. **Calculate the total amount saved by Lilly:**
Lilly saves \$2 each day for 22 days.
\[
\text{Total Savings} = \$2/day \times 22\ days = \$44
\]
2. **Determine how many flowers Lilly can buy:**
Each flower costs \$4.
\[
\text{Number of Flowers} = \frac{\$44}{\$4/f... |
orca_math | Scott has 7 pairs of shoes. Anthony has 3 times as many pairs of shoes as Scott, and Jim has 2 less pairs than Anthony. How many more pairs of shoes does Anthony have compared to Jim? | First, determine the number of pairs of shoes Anthony has by multiplying Scott's pairs by 3.
Next, find out how many pairs Jim has by subtracting 2 from Anthony's total.
Finally, calculate the difference between Anthony's and Jim's pairs of shoes to determine how many more pairs Anthony has compared to Jim. | Let's solve the problem step by step.
1. **Determine the number of pairs Anthony has:**
Anthony has 3 times as many pairs of shoes as Scott.
\[
\text{Anthony's pairs} = 3 \times \text{Scott's pairs} = 3 \times 7 = 21
\]
2. **Determine the number of pairs Jim has:**
Jim has 2 less pairs than... |
orca_math | Katie had 81 DS games and her friends had some games. Katie has 22 more games than her friends. How many DS games do her friends have? | First, I need to determine how many DS games Katie's friends have. I know that Katie has a total of 81 DS games and that she has 22 more games than her friends.
To find out how many games her friends have, I can set up an equation where the number of games her friends have is represented by \( F \).
According to the ... | **Solution:**
Let's determine how many DS games Katie's friends have.
1. **Define the Variables:**
- Let \( F \) represent the number of DS games Katie's friends have.
- Katie has 81 DS games.
2. **Set Up the Equation:**
- According to the problem, Katie has 22 more games than her friends. This can be expre... |
gsm8k | John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get? | First, I need to determine the total length of fishing line John has. He buys 3 reels, each containing 100 meters of fishing line.
Next, I'll calculate the total length by multiplying the number of reels by the length of each reel:
3 reels × 100 meters per reel = 300 meters.
Now, John wants to cut this fishing line i... | **Solution:**
1. **Determine the total length of fishing line:**
John buys **3 reels** of fishing line, each reel being **100 meters** long.
\[
\text{Total length} = 3 \times 100\, \text{m} = 300\, \text{m}
\]
2. **Calculate the number of 10-meter sections:**
He cuts the total length into s... |
synthetic_amc | A small village has a total population of $520$. The data is shown on a graph which divides this population into four equal groups represented by rectangles. However, the labels specifying males and females are unreaded. If it is known that one rectangle represents all males in the village, how many males are there?
$\... | To determine the number of males in the village, we start by noting that the total population is 520 and it is divided into four equal groups. Each group is represented by a rectangle on the graph.
Since the population is divided equally, each group (rectangle) represents:
\[
\frac{520}{4} = 130
\]
Given that one of ... | To determine the number of males in the village, let's analyze the given information step by step.
1. **Total Population**: The village has a total population of **520**.
2. **Division into Groups**: The population is divided into **four equal groups**, each represented by a rectangle on the graph.
3. **Equal Group ... |
synthetic_amc | On a number line where the markings are equally spaced, what is the number $x$ if nine steps are taken to get from 0 to 36?
$\text{(A)}\ 20 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 28 \qquad \text{(D)}\ 32 \qquad \text{(E)}\ 36$ | First, I need to determine the length of each step on the number line. Since there are nine steps from 0 to 36, I can calculate the length of each step by dividing the total distance by the number of steps.
Next, I'll use the length of each step to find the number \( x \) that is reached after taking six steps from 0.... | To determine the number \( x \) on a number line where the markings are equally spaced and nine steps are taken to get from 0 to 36, follow these steps:
1. **Calculate the length of each step:**
Since there are nine steps from 0 to 36, the length of each step is:
\[
\text{Step length} = \frac{36}{9} = 4
... |
cn_k12 | Given points A(1, -1) and B(1, 2), then $\overrightarrow{AB} = $ ______. | First, identify the coordinates of points A and B. Point A is at (1, -1) and point B is at (1, 2).
To find the vector \(\overrightarrow{AB}\), subtract the coordinates of point A from the coordinates of point B.
Calculate the x-component of the vector:
\[
1 - 1 = 0
\]
Calculate the y-component of the vector:
\[
2 - ... | To find the vector \(\overrightarrow{AB}\) given points \(A(1, -1)\) and \(B(1, 2)\), follow these steps:
1. **Understand the Vector Representation:**
The vector \(\overrightarrow{AB}\) is calculated by subtracting the coordinates of point \(A\) from the coordinates of point \(B\).
2. **Apply the Vector Formul... |
orca_math | Jesse has 21 bananas. If he shares them among 3 friends, each friend would get _____ bananas . | I need to determine how many bananas each of Jesse's 3 friends will receive if he shares his 21 bananas equally among them.
First, I'll identify the total number of bananas, which is 21.
Next, I'll determine the number of friends, which is 3.
To find out how many bananas each friend gets, I'll divide the total numbe... | **Solution:**
Jesse has a total of **21 bananas** and wants to share them equally among **3 friends**. To find out how many bananas each friend will receive, we can use the division operation.
\[
\text{Number of bananas per friend} = \frac{\text{Total number of bananas}}{\text{Number of friends}} = \frac{21}{3}
\]
\... |
orca_math | When 632-AB1=41, what number should go in B? | First, I need to understand the equation \(632 - AB1 = 41\). Here, \(AB1\) represents a three-digit number where \(A\) and \(B\) are digits.
To isolate \(AB1\), I'll subtract 41 from 632:
\[
632 - 41 = 591
\]
So, \(AB1 = 591\).
Next, I'll compare the digits of \(AB1\) with 591:
- The hundreds place: \(A = 5\)
- The t... | To determine the value of \( B \) in the equation:
\[
632 - AB1 = 41
\]
follow these steps:
1. **Isolate \( AB1 \):**
\[
AB1 = 632 - 41
\]
\[
AB1 = 591
\]
2. **Compare the digits:**
- **Hundreds place:** \( A = 5 \)
- **Tens place:** \( B = 9 \)
- **Ones place:** \( 1 = 1 \)
3. **C... |
orca_math | Anais has 30 more toys than Kamari. Kamari has 65 toys in his box. How many toys are there altogether? | First, I note that Kamari has 65 toys.
Since Anais has 30 more toys than Kamari, I add 30 to Kamari's number of toys to find out how many toys Anais has.
So, Anais has 65 + 30 = 95 toys.
To find the total number of toys altogether, I add the number of toys Kamari has to the number of toys Anais has.
Therefore, the ... | **Solution:**
1. **Determine the number of toys Anais has:**
Anais has 30 more toys than Kamari. Since Kamari has 65 toys, we can calculate Anais's toys as follows:
\[
\text{Anais's toys} = \text{Kamari's toys} + 30 = 65 + 30 = 95
\]
2. **Calculate the total number of toys:**
To find the total nu... |
cn_k12 | In a health survey conducted by a certain school involving 1,200 male and female students, a stratified sampling method was used to draw a sample of 200 students. It is known that 85 females were sampled. The number of male students in the school is _______. | First, determine the proportion of the sample relative to the total population. Since 200 students were sampled out of 1,200, the sampling ratio is 1/6.
Next, calculate the total number of female students in the school by multiplying the number of sampled females (85) by the sampling ratio (6):
F = 85 × 6 = 510.
Fina... | To determine the number of male students in the school, let's follow these steps:
1. **Understand the Sampling Ratio:**
- **Total Students:** 1,200
- **Sample Size:** 200
- **Sampling Ratio:** \(\frac{200}{1200} = \frac{1}{6}\)
2. **Determine the Number of Female Students:**
- **Sampled Females:** 85
-... |
orca_math | Sally had 27 Pokemon cards. Dan has some new Pokemon cards. Sally bought 20 Pokemon cards. Now, Sally has 6 more Pokemon cards than Dan has. How many Pokemon cards does Dan have? | First, determine the total number of Pokémon cards Sally has after her purchase. She initially had 27 cards and bought 20 more, so she now has 47 cards.
Next, set up an equation where Sally's total cards are equal to Dan's cards plus 6, since Sally has 6 more cards than Dan. This gives the equation 47 = D + 6.
Finall... | Let's solve the problem step by step.
**Given:**
- Sally initially has **27** Pokémon cards.
- Dan has an unknown number of Pokémon cards, which we'll denote as **\( D \)**.
- Sally buys **20** additional Pokémon cards.
- After the purchase, Sally has **6** more Pokémon cards than Dan.
**Step 1: Calculate Sally's Tot... |
orca_math | A boy has 12 oranges. He gives one-third of this number to his brother, a fraction of the remainder to his friend, and keeps the rest for himself. His friend gets 2 oranges. What is the ratio of the number of oranges given to his friend to the remainder after giving some to his brother? | First, determine how many oranges the boy gives to his brother by calculating one-third of 12.
Next, subtract the number of oranges given to the brother from the total to find the remainder.
Then, identify the number of oranges given to the friend, which is provided as 2.
Finally, calculate the ratio of the oranges ... | **Solution:**
Let's break down the problem step by step.
1. **Total Oranges:**
\[
\text{Total oranges} = 12
\]
2. **Oranges Given to Brother:**
\[
\text{Oranges given to brother} = \frac{1}{3} \times 12 = 4
\]
3. **Remaining Oranges After Giving to Brother:**
\[
\text{Remaining oranges} = 12... |
synthetic_math | If \( f(x) = 5 - 4x \) and \( g(x) = x^2 + 2 \), find \( f(g(2)) \). | First, I need to find the value of \( g(2) \). The function \( g(x) \) is given as \( x^2 + 2 \). So, substituting \( x = 2 \) into \( g(x) \), I get:
\[ g(2) = 2^2 + 2 = 4 + 2 = 6 \]
Next, I need to find \( f(g(2)) \), which is \( f(6) \). The function \( f(x) \) is given as \( 5 - 4x \). Substituting \( x = 6 \) in... | To find \( f(g(2)) \) given the functions \( f(x) = 5 - 4x \) and \( g(x) = x^2 + 2 \), follow these steps:
1. **Calculate \( g(2) \):**
\[
g(2) = (2)^2 + 2 = 4 + 2 = 6
\]
2. **Substitute \( g(2) \) into \( f(x) \):**
\[
f(g(2)) = f(6) = 5 - 4(6) = 5 - 24 = -19
\]
**Final Answer:**
\[
\boxed{-19... |
orca_math | At the presentation, students take turns giving presentations. Eunjung will be the 6th speaker from the back, and the seven students in front of Eunjung will make the presentation. How many students are giving presentations? | First, I recognize that Eunjung is the 6th speaker from the back, which means there are 5 students behind her.
Next, there are 7 students in front of Eunjung who will give presentations.
To find the total number of students giving presentations, I add the number of students in front of Eunjung, Eunjung herself, and t... | To determine the total number of students giving presentations, let's break down the information provided:
1. **Eunjung's Position from the Back:**
- Eunjung is the **6th speaker from the back**.
- This means there are **5 students** behind her.
2. **Students in Front of Eunjung:**
- There are **7 students**... |
orca_math | The cash realized on selling a 14% stock is Rs. 109.25. The cash amount before brokerage is Rs. 109. What is the percentage of the brokerage? | First, I need to determine the difference between the cash realized on selling the stock and the cash amount before brokerage. This difference will represent the amount of brokerage paid.
Next, I'll calculate the percentage of the brokerage by dividing the brokerage amount by the cash amount before brokerage and then ... | To determine the percentage of the brokerage, follow these steps:
1. **Calculate the Brokerage Amount:**
The difference between the cash realized and the cash amount before brokerage is the brokerage amount.
\[
\text{Brokerage Amount} = \text{Cash Realized} - \text{Cash Amount Before Brokerage} = 109.25 - 1... |
orca_math | You have collected 7 crickets. How many more crickets do you need to collect to have a certain number of crickets if you need to collect 4 more? | First, I need to determine the total number of crickets desired. The user has already collected 7 crickets and needs to collect 4 more.
To find the total number of crickets needed, I add the number of crickets already collected to the number of additional crickets required.
So, 7 crickets (already collected) plus 4 c... | To determine how many more crickets you need to collect, let's break down the problem step by step.
**Given:**
- You have already collected **7 crickets**.
- You need to collect **4 more crickets**.
**Calculation:**
1. **Total Crickets Needed:**
To find the total number of crickets you want to have, add the numb... |
gsm8k | Ken created a care package to send to his brother, who was away at boarding school. Ken placed a box on a scale, and then he poured into the box enough jelly beans to bring the weight to 2 pounds. Then, he added enough brownies to cause the weight to triple. Next, he added another 2 pounds of jelly beans. And final... | First, Ken adds jelly beans to the box until it weighs 2 pounds.
Next, he adds brownies, tripling the weight to 6 pounds.
Then, he adds another 2 pounds of jelly beans, making the total weight 8 pounds.
Finally, he adds gummy worms, doubling the weight to 16 pounds. | Let's break down the process step by step to determine the final weight of the box of goodies.
1. **Adding Jelly Beans:**
- Ken starts by adding jelly beans until the box weighs **2 pounds**.
2. **Adding Brownies:**
- He then adds brownies, which triples the current weight.
\[
\text{New Weight} = 2 \, ... |
orca_math | It is 78 miles to Grandma's house. Mr. Welch drove 35 miles. He stopped to buy a pie for dessert. Then he drove 18 miles and stopped to put gas in the car. How many more miles until he reaches Grandma's house? | First, I need to determine the total distance Mr. Welch has already driven. He initially drove 35 miles and then drove an additional 18 miles after stopping for a pie. Adding these together gives a total of 53 miles driven so far.
Next, I will subtract the distance he has already covered from the total distance to Gra... | **Solution:**
To determine how many more miles Mr. Welch needs to drive to reach Grandma's house, follow these steps:
1. **Calculate the total miles driven so far:**
- First leg: 35 miles
- Second leg: 18 miles
\[
\text{Total miles driven} = 35 \text{ miles} + 18 \text{ miles} = 53 \text{ miles}
\... |
orca_math | Dilan, Martha, Phillip, and Veronica went to the park together to have some fun. They all had a different number of marbles. At the end of the day, they redistributed the marbles so they each had 15 marbles. If Dilan had 14 marbles, Martha had 20 marbles, and Veronica had 7 marbles, how many marbles did Phillip have in... | First, determine the total number of marbles after redistribution by multiplying the number of friends by the marbles each had:
4 friends × 15 marbles each = 60 marbles.
Next, add the initial marbles of Dilan, Martha, and Veronica:
14 (Dilan) + 20 (Martha) + 7 (Veronica) = 41 marbles.
Finally, subtract the sum of the... | To determine how many marbles Phillip initially had, let's follow these steps:
1. **Calculate the Total Number of Marbles After Redistribution:**
Since each of the four friends ended up with 15 marbles after redistribution:
\[
\text{Total marbles} = 4 \times 15 = 60 \text{ marbles}
\]
2. **Sum the Ini... |
orca_math | What is the least number that should be added to some number, so the sum of the number is completely divisible by 23? The answer is 4. What is the original number? | To determine the original number, let's denote it as \( x \). The problem states that when 4 is added to \( x \), the sum is completely divisible by 23. This can be expressed mathematically as:
\[
x + 4 \equiv 0 \mod 23
\]
To find \( x \), we can rearrange the equation:
\[
x \equiv -4 \mod 23
\]
Since we are lookin... | To determine the original number, let's denote it as \( x \). The problem states that when 4 is added to \( x \), the sum is completely divisible by 23. This can be expressed mathematically as:
\[
x + 4 \equiv 0 \mod 23
\]
To find \( x \), we can rearrange the equation:
\[
x \equiv -4 \mod 23
\]
Since we are lookin... |
cn_k12 | The imaginary part of the complex number $z=2-i$ is ( )
A: 2
B: 1
C: -1
D: -i | To determine the imaginary part of the complex number \( z = 2 - i \), I start by recalling the standard form of a complex number, which is \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.
In the given complex number \( z = 2 - i \), the real part is clearly \( 2 \). The imaginary part i... | To determine the imaginary part of the complex number \( z = 2 - i \), let's analyze its components.
A complex number is generally expressed in the form:
\[
z = a + bi
\]
where:
- \( a \) is the **real part**,
- \( b \) is the **imaginary part**,
- \( i \) is the imaginary unit with the property \( i^2 = -1 \).
Given... |
cn_k12 | A school is recruiting announcers for the sports day. One person will be randomly selected from three boys and one girl. The probability of selecting the girl is ( ).
A: $\frac{1}{2}$
B: $\frac{1}{3}$
C: $\frac{1}{4}$
D: $\frac{1}{5}$ | To determine the probability of selecting the girl from the group of candidates for the announcer position, follow these steps:
1. **Calculate the Total Number of Candidates**:
- Number of boys: 3
- Number of girls: 1
- Total candidates = 3 boys + 1 girl = 4 candidates
2. **Determine the Number of Favorable ... | To determine the probability of selecting the girl from the group of candidates for the announcer position, follow these steps:
1. **Calculate the Total Number of Candidates**:
- Number of boys: 3
- Number of girls: 1
- **Total candidates** = 3 boys + 1 girl = **4 candidates**
2. **Determine the Number of Fa... |
orca_math | How much is 80% of 45 greater than 4/5 of 25? | First, I need to calculate 80% of 45. To do this, I'll convert the percentage to a decimal by dividing by 100, which gives me 0.80. Then, I'll multiply 0.80 by 45 to find the value.
Next, I'll calculate 4/5 of 25. To simplify this, I'll divide 25 by 5 to get 5, and then multiply by 4 to find the result.
Finally, I'll... | **Solution:**
We need to determine how much greater 80% of 45 is compared to \(\frac{4}{5}\) of 25.
1. **Calculate 80% of 45:**
\[
80\% \text{ of } 45 = 0.80 \times 45 = 36
\]
2. **Calculate \(\frac{4}{5}\) of 25:**
\[
\frac{4}{5} \text{ of } 25 = \frac{4}{5} \times 25 = \frac{100}{5} = 20
\]
3. **Find the differ... |
orca_math | Danielle's apartment has 6 rooms. Heidi's apartment has 3 times as many rooms as Danielle's apartment. Grant's apartment has 1/9 as many rooms as Heidi's apartment. How many rooms does Grant's apartment have? | First, I need to determine the number of rooms in Heidi's apartment. Since Heidi's apartment has 3 times as many rooms as Danielle's, I multiply the number of rooms in Danielle's apartment by 3.
Next, I calculate the number of rooms in Grant's apartment. Grant's apartment has 1/9 as many rooms as Heidi's, so I divide ... | Let's solve the problem step by step.
1. **Danielle's Apartment:**
- Danielle's apartment has **6 rooms**.
2. **Heidi's Apartment:**
- Heidi's apartment has **3 times** as many rooms as Danielle's.
- Calculation:
\[
3 \times 6 = 18
\]
- **Heidi's apartment has 18 rooms.**
3. **Grant's Apar... |
orca_math | A group of 5 friends went into a restaurant. The chef already had 20 chicken wings cooked but cooked 25 more for the group. If they each got the same amount, how many would each person get? | First, I need to determine the total number of chicken wings available. The chef already had 20 chicken wings cooked and cooked an additional 25 for the group. Adding these together gives a total of 45 chicken wings.
Next, I need to divide the total number of chicken wings equally among the 5 friends. By dividing 45 b... | **Solution:**
Let's determine how many chicken wings each of the 5 friends would receive.
1. **Calculate the total number of chicken wings:**
The chef had 20 chicken wings already cooked and cooked an additional 25 for the group.
\[
\text{Total chicken wings} = 20 + 25 = 45
\]
2. **Distribute the... |
gsm8k | The cost of a slice of cake is three-fourths of the cost of a cup of milk tea. If the milk tea costs $2.40, how much do 2 slices of cake and 1 cup of milk tea cost? | First, I need to determine the cost of one slice of cake. The problem states that a slice of cake costs three-fourths of a cup of milk tea. Given that a cup of milk tea costs $2.40, I can calculate the cost of a slice of cake by multiplying $2.40 by 3/4.
Next, I'll find the cost for two slices of cake by multiplying t... | To determine the total cost of 2 slices of cake and 1 cup of milk tea, follow these steps:
1. **Find the cost of one slice of cake:**
The cost of a slice of cake is three-fourths the cost of a cup of milk tea.
\[
\text{Cost of one slice of cake} = \frac{3}{4} \times \$2.40 = \$1.80
\]
2. **Calculate the... |
orca_math | She estimated the number of candies that she will receive from each block. If she will receive around 7 pieces of candies from every house, and there are some houses in a block, she will receive 35 candies from each block. How many houses are in a block? | To determine the number of houses in a block, I start by noting that she receives 7 pieces of candy from each house.
She estimates receiving a total of 35 candies from each block.
To find the number of houses, I divide the total number of candies by the number of candies received per house.
This calculation is 35 ca... | To determine the number of houses in a block, follow these steps:
1. **Identify the total number of candies received from one block:**
\[
\text{Total candies per block} = 35 \text{ candies}
\]
2. **Determine the number of candies received from each house:**
\[
\text{Candies per house} = 7 \text... |
synthetic_amc | Find the value range for $\sqrt{224}$. The options are:
$\text{(A)}\ 14 \qquad \text{(B)}\ \text{less than }14 \qquad \text{(C)}\ \text{between }14\text{ and }15 \qquad \text{(D)}\ \text{between }15\text{ and }16 \qquad \text{(E)}\ \text{between }16\text{ and }17$
$\text{(A)}\ 14 \qquad \text{(B)}\ \text{less than }14 ... | To determine the value range for \(\sqrt{224}\), we can follow these steps:
1. **Identify nearby perfect squares**: The perfect squares closest to 224 are 196 (\(14^2\)) and 225 (\(15^2\)).
2. **Compare 224 with these perfect squares**: Since \(196 < 224 < 225\), it follows that:
\[
14 < \sqrt{224} < 15
\]
... | To determine the value range for \(\sqrt{224}\), let's analyze the given options step by step.
1. **Identify Nearby Perfect Squares**:
- \(14^2 = 196\)
- \(15^2 = 225\)
2. **Compare 224 with These Perfect Squares**:
- Since \(196 < 224 < 225\), it follows that:
\[
14 < \sqrt{224} < 15
\]
3. *... |
gsm8k | Stacy has 2 more than triple as many berries as Steve. Steve has one half as many berries as Skylar. If Skylar has 20 berries, how many berries does Stacy have? | First, determine the number of berries Steve has. Since Steve has one half as many berries as Skylar, and Skylar has 20 berries, Steve has \( \frac{1}{2} \times 20 = 10 \) berries.
Next, calculate the number of berries Stacy has. Stacy has 2 more than triple the number of berries Steve has. Therefore, Stacy has \( 2 +... | **Solution:**
Let's break down the problem step by step.
1. **Determine the number of berries Steve has:**
Steve has one half as many berries as Skylar.
\[
\text{Steve's berries} = \frac{1}{2} \times \text{Skylar's berries} = \frac{1}{2} \times 20 = 10
\]
2. **Determine the number of berries Stacy h... |
orca_math | James has 28 marbles. He puts them into 4 bags. He puts the same number in each bag. He then gives away some bags. James has 21 marbles left. How many bags did James give away? | First, determine the number of marbles in each bag by dividing the total number of marbles by the number of bags.
Next, calculate how many marbles James has given away by subtracting the remaining marbles from the total number of marbles.
Finally, find out how many bags James gave away by dividing the number of marbl... | **Solution:**
1. **Determine the number of marbles in each bag:**
James has a total of 28 marbles and he puts them equally into 4 bags.
\[
\text{Marbles per bag} = \frac{28}{4} = 7
\]
2. **Calculate the number of marbles James gave away:**
James has 21 marbles left after giving away some bags.
\... |
orca_math | Mom, Dad, and Grandpa bought clothes at the department store. Dad bought more clothes than Mom, and Grandpa bought more clothes than Dad. If you lined up people based on the number of clothes they bought in ascending order, in what position will Mom be? Please answer using an natural number. | First, I need to understand the relationships between the number of clothes each person bought. It's given that Dad bought more clothes than Mom, and Grandpa bought more clothes than Dad.
This means the order from least to most clothes bought is Mom, then Dad, and finally Grandpa.
When arranging them in ascending ord... | Let's determine the position of Mom when lining up the people based on the number of clothes they bought in ascending order.
### Given:
1. **Dad bought more clothes than Mom.**
2. **Grandpa bought more clothes than Dad.**
### Step-by-Step Analysis:
1. **Determine the Order of Clothes Bought:**
- From the given inf... |
cn_k12 | Compare the numbers: $-9\_\_\_\_\_\_-2$ (Fill in the blank with $ \lt $ or $ \gt $). | To compare the numbers \(-9\) and \(-2\), I start by understanding that both are negative numbers. In the context of negative numbers, the number with the larger absolute value is actually smaller.
First, I determine the absolute values:
- The absolute value of \(-9\) is \(|-9| = 9\).
- The absolute value of \(-2\) i... | To compare the numbers \(-9\) and \(-2\), follow these steps:
1. **Understand Negative Numbers:**
- Negative numbers decrease in value as their magnitude increases.
- On the number line, \(-9\) is to the left of \(-2\), indicating that \(-9\) is smaller than \(-2\).
2. **Compare the Magnitudes:**
- The absol... |
orca_math | The income and expenditure of a person are in the ratio 7 : 6. If the person saves Rs. 3000, what is his income? | First, I recognize that the income and expenditure are in the ratio 7:6. This means I can represent the income as 7 times a common variable and the expenditure as 6 times the same variable.
Next, I know that savings are calculated by subtracting expenditure from income. The problem states that the savings amount to Rs... | **Solution:**
Let's denote the income and expenditure of the person as follows:
- **Income** = \( 7x \)
- **Expenditure** = \( 6x \)
where \( x \) is a common multiplier.
According to the problem, the person saves Rs. 3000. Savings can be calculated as:
\[
\text{Savings} = \text{Income} - \text{Expenditure}
\]
Su... |
orca_math | The Ferris wheel in paradise park has 3 small seats and 7 large seats. Each small seat can hold 16 people and each large seat can hold 12 people. How many people can ride the Ferris wheel on large seats? | First, identify the number of large seats available on the Ferris wheel, which is 7.
Next, determine the capacity of each large seat, which is 12 people.
To find the total number of people that can ride on the large seats, multiply the number of large seats by the capacity of each large seat.
So, 7 large seats multi... | **Solution:**
To determine how many people can ride the Ferris wheel on large seats, follow these steps:
1. **Identify the number of large seats:**
\[
\text{Number of large seats} = 7
\]
2. **Determine the capacity of each large seat:**
\[
\text{Capacity per large seat} = 12 \text{ people}
... |
orca_math | A train 140 meters long crosses an electric pole in 2.3998080153587713 seconds, if its speed is a certain km/hr. What is the speed of the train? | First, I need to determine the speed of the train in meters per second by dividing the length of the train by the time it takes to cross the electric pole.
Next, I'll convert the speed from meters per second to kilometers per hour using the conversion factor of 3.6.
Finally, I'll present the calculated speed in kilom... | To determine the speed of the train, we'll follow these steps:
1. **Calculate the speed in meters per second (m/s):**
The train crosses an electric pole, meaning it covers a distance equal to its own length.
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{140 \text{ meters}}{2.399808015358771... |
synthetic_math | We have that $3a + 2 = 2$ and $b - 2a = 3.$ What is the value of $b$? | First, I need to solve the equation \(3a + 2 = 2\) to find the value of \(a\).
Subtracting 2 from both sides gives:
\[
3a = 0
\]
Then, dividing both sides by 3:
\[
a = 0
\]
Next, I substitute \(a = 0\) into the second equation \(b - 2a = 3\):
\[
b - 2(0) = 3
\]
Simplifying:
\[
b = 3
\]
Therefore, the value of \(b\)... | To find the value of \( b \), follow these steps:
1. **Solve for \( a \) using the first equation:**
\[
3a + 2 = 2
\]
Subtract 2 from both sides:
\[
3a = 0
\]
Divide both sides by 3:
\[
a = 0
\]
2. **Substitute \( a = 0 \) into the second equation to find \( b \):**
\[
b - 2a = ... |
orca_math | A pet shelter had 10 puppies when another 15 were brought in. If 7 puppies a day are adopted, how long would it take for all of them to be adopted? | First, I need to determine the total number of puppies at the shelter. Initially, there are 10 puppies, and another 15 are brought in. Adding these together gives a total of 25 puppies.
Next, I know that 7 puppies are adopted each day. To find out how many days it will take for all 25 puppies to be adopted, I divide t... | **Solution:**
Let's determine how many days it will take for all the puppies to be adopted.
1. **Calculate the total number of puppies:**
\[
\text{Initial puppies} + \text{Additional puppies} = 10 + 15 = 25 \text{ puppies}
\]
2. **Determine the number of days required for adoption:**
\[
\text{... |
orca_math | A chef served 3 different foods for a banquet: 25 plates of lobster rolls, 14 plates of spicy hot noodles, and some plates of seafood noodles. The chef made 55 plates of food altogether. How many plates of seafood noodles did the chef make? | First, I need to determine the total number of plates the chef made, which is 55.
Next, I'll add the number of plates of lobster rolls and spicy hot noodles: 25 + 14 = 39.
Finally, I'll subtract this sum from the total number of plates to find out how many plates of seafood noodles were made: 55 - 39 = 16.
Therefore... | To determine how many plates of seafood noodles the chef made, follow these steps:
1. **Identify the total number of plates:**
\[
\text{Total plates} = 55
\]
2. **Determine the number of plates for the other two foods:**
\[
\text{Lobster rolls} = 25
\]
\[
\text{Spicy hot noodles} = 14
\]
3... |
synthetic_math | Subtract $444.44$ from $888.88$. Express the result as a decimal to the nearest hundredth. | To subtract 444.44 from 888.88, I will first align the numbers by their decimal points to ensure each digit is in the correct place value.
Starting with the hundredths place, I subtract 4 from 8, which gives me 4. Moving to the tenths place, I subtract another 4 from 8, resulting in 4. In the ones place, subtracting 4... | To subtract \(444.44\) from \(888.88\), follow these steps:
1. **Align the numbers by their decimal points:**
\[
\begin{array}{r}
\ \ 888.88 \\
-444.44 \\
\hline
\end{array}
\]
2. **Subtract each corresponding digit starting from the right:**
\[
\begin{array}{r}
\ \ 888.88 \\
-444.44 \\
\hline
\ \ 444.44 \\
\end{ar... |
orca_math | Edward was trying to expand his game collection. He bought 41 games from a friend and bought 14 more at a garage sale. If 31 of the games didn't work, how many good games did he end up with? | First, I need to determine the total number of games Edward purchased. He bought 41 games from a friend and an additional 14 games at a garage sale.
Next, I'll add these two quantities together to find the total number of games:
41 games + 14 games = 55 games.
Edward found out that 31 of these games didn't work. To f... | **Solution:**
Let's break down the problem step by step to find out how many good games Edward ended up with.
1. **Total Games Purchased:**
- **From a friend:** 41 games
- **From a garage sale:** 14 games
\[
\text{Total games} = 41 + 14 = 55 \text{ games}
\]
2. **Games That Didn't Work:**
... |
orca_math | In a football game, wristbands were given to every spectator for both their hands. In total 234 wristbands were distributed. How many people watched the game? | First, I need to determine how many wristbands each spectator received. The problem states that wristbands were given to every spectator for both their hands, which means each person received 2 wristbands.
Next, I'll use the total number of wristbands distributed, which is 234, to find out how many people attended the... | To determine how many people watched the game, let's break down the problem step by step.
**Given:**
- Each spectator received **2 wristbands** (one for each hand).
- The **total number of wristbands distributed** was **234**.
**Step 1: Understand the Distribution**
- Every person received **2 wristbands**.
**Step 2... |
synthetic_math | Compute: $12 \cdot \frac{1}{15} \cdot 30.$ | First, I need to compute the expression \(12 \cdot \frac{1}{15} \cdot 30\).
I can start by simplifying the multiplication of the fractions and the whole numbers. Multiplying \(\frac{1}{15}\) by 30 gives me \(\frac{30}{15}\), which simplifies to 2.
Now, the expression becomes \(12 \cdot 2\). Multiplying 12 by 2 result... | To compute \(12 \cdot \frac{1}{15} \cdot 30\), follow these steps:
1. **Multiply the fractions and whole numbers:**
\[
12 \cdot \frac{1}{15} \cdot 30
\]
2. **Simplify the multiplication of \(\frac{1}{15}\) and 30:**
\[
\frac{1}{15} \cdot 30 = \frac{30}{15} = 2
\]
3. **Now, multiply 12 by the result... |
orca_math | A train 500 m long can cross an electric pole in 20 seconds. Find the speed of the train. | First, I need to determine the speed of the train using the information provided.
The train is 500 meters long and crosses an electric pole in 20 seconds. When the train crosses the pole, it travels a distance equal to its own length.
So, the distance traveled is 500 meters, and the time taken is 20 seconds.
To find... | To determine the speed of the train, we can use the basic formula for speed:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
**Given:**
- Length of the train (\(D\)) = 500 meters
- Time taken to cross the electric pole (\(T\)) = 20 seconds
**Step 1:** Understand that when the train crosses the electric pole... |
synthetic_math | The Ponde family's Powerjet pumps 500 gallons of water per hour. At this rate, how many gallons of water will it pump in 30 minutes? | First, recognize that the pumping rate is 500 gallons per hour.
Next, determine the fraction of an hour that 30 minutes represents. Since there are 60 minutes in an hour, 30 minutes is half of an hour, or 0.5 hours.
Finally, multiply the pumping rate by the time to find the total volume of water pumped:
500 gallons/h... | To determine how many gallons of water the Ponde family's Powerjet will pump in **30 minutes**, follow these steps:
1. **Understand the Pumping Rate:**
The Powerjet pumps **500 gallons per hour**.
2. **Convert Minutes to Hours:**
Since there are **60 minutes** in an hour, **30 minutes** is:
\[
\fr... |
gsm8k | Joel’s garden is 64 square feet large. He wants to use half of the garden for fruits and half of the garden for vegetables. He wants to use a quarter of the fruit section for strawberries. How many square feet of the garden will be used for strawberries? | First, I need to determine the total area of Joel's garden, which is given as 64 square feet.
Joel plans to divide his garden equally between fruits and vegetables. Therefore, I will calculate the area allocated for fruits by dividing the total area by 2:
64 ÷ 2 = 32 square feet.
Next, Joel wants to use a quarter of ... | **Solution:**
1. **Total Garden Area:**
Joel's garden has a total area of:
\[
64 \text{ square feet}
\]
2. **Area Allocated for Fruits:**
Joel wants to use half of the garden for fruits. Therefore, the area for fruits is:
\[
\frac{64}{2} = 32 \text{ square feet}
\]
3. **Area Allocated... |
orca_math | if 20 % of a number = 200 , then 120 % of that number will be ? | First, I need to find the number when 20% of it equals 200. To do this, I'll set up the equation 0.20 * x = 200, where x is the unknown number.
Next, I'll solve for x by dividing both sides of the equation by 0.20. This gives me x = 200 / 0.20, which simplifies to x = 1000.
Now that I know the number is 1000, I can f... | **Solution:**
We are given that **20%** of a number equals **200**. Let's denote the unknown number as \( x \).
1. **Set up the equation:**
\[
20\% \times x = 200
\]
This can be written as:
\[
0.20 \times x = 200
\]
2. **Solve for \( x \):**
\[
x = \frac{200}{0.20}
\]
... |
cn_k12 | In the Cartesian coordinate system, the distance from the point $\left(3,-2\right)$ to the origin is ______. | To find the distance from the point \((3, -2)\) to the origin in the Cartesian coordinate system, I will use the distance formula. The distance \(d\) from a point \((x, y)\) to the origin \((0, 0)\) is given by:
\[
d = \sqrt{x^2 + y^2}
\]
Substituting the given coordinates \(x = 3\) and \(y = -2\) into the formula:
... | To find the distance from the point \((3, -2)\) to the origin in the Cartesian coordinate system, we use the distance formula. The distance \(d\) from a point \((x, y)\) to the origin \((0, 0)\) is given by:
\[
d = \sqrt{x^2 + y^2}
\]
Substituting the given coordinates \(x = 3\) and \(y = -2\) into the formula:
\[
d... |
orca_math | Eric has a chicken farm with some chickens. His chickens lay 3 eggs each day. After 3 days, Eric collected 36 eggs. How many chickens does Eric have on his farm? | First, I need to determine the total number of eggs laid by all the chickens over the 3 days. Eric collected 36 eggs in total.
Next, I'll calculate the number of eggs laid per day by dividing the total eggs by the number of days: 36 eggs ÷ 3 days = 12 eggs per day.
Since each chicken lays 3 eggs per day, I can find o... | To determine how many chickens Eric has on his farm, let's break down the problem step by step.
**Given:**
- Each chicken lays **3 eggs** per day.
- After **3 days**, Eric collected a total of **36 eggs**.
**Step 1: Calculate the Total Number of Eggs Laid Per Day**
First, find out how many eggs are laid by all the c... |
orca_math | Paul made forty-four dollars mowing lawns and some money weed eating. If he only spent nine dollars a week, the money would last him 8 weeks. How much money did he make weed eating? | Okay, let's see. So, Paul made some money mowing lawns and some money weed eating. He made $44 from mowing lawns, and we don't know how much he made from weed eating. But we do know that if he spends $9 a week, his money will last him 8 weeks. So, I need to figure out how much he made from weed eating.
First, maybe I ... | Paul made $28 from weed eating. |
cn_k12 | If "$8$ in row $4$" is denoted as $\left(8,4\right)$, then "$3$ in row $5$" is denoted as ____. | First, I need to understand the notation provided. The phrase "$8$ in row $4$" is denoted as $\left(8,4\right)$. This indicates that the first number represents the element or number itself, and the second number represents the row in which this element is located.
Next, I apply this understanding to the new phrase "$... | To determine how to denote "$3$ in row $5$" based on the given notation, let's follow the pattern established by the example:
1. **Understanding the Given Notation:**
- The phrase "$8$ in row $4$" is denoted as $\left(8,4\right)$.
- Here, the **first number** represents the **element** or **number**, and the **s... |
orca_math | Will was organizing his baseball cards in a binder with 3 on each page. He had 8 new cards and 10 old cards to put in the binder. How many pages would he use? | First, I need to determine the total number of baseball cards Will has. He has 8 new cards and 10 old cards.
Next, I'll add the number of new and old cards together to find the total number of cards:
8 new cards + 10 old cards = 18 cards
Now, I know that Will can place 3 cards on each page of the binder. To find out ... | **Solution:**
To determine how many pages Will will use to organize his baseball cards, follow these steps:
1. **Calculate the total number of cards:**
\[
\text{Total cards} = \text{New cards} + \text{Old cards} = 8 + 10 = 18 \text{ cards}
\]
2. **Determine the number of pages needed:**
Since Wil... |
orca_math | Marcella has 27 pairs of shoes. If she loses some individual shoes, the greatest number of matching pairs she could have left is 22. How many individual shoes did she lose? | First, calculate the total number of individual shoes Marcella originally has by multiplying the number of pairs by 2: 27 pairs × 2 = 54 individual shoes.
Next, determine the number of individual shoes that remain after losing some. If she has 22 pairs left, that means she has 22 × 2 = 44 individual shoes still in pai... | **Solution:**
Marcella initially has **27 pairs** of shoes. Since each pair consists of 2 individual shoes, the total number of individual shoes she has is:
\[
27 \text{ pairs} \times 2 = 54 \text{ individual shoes}
\]
After losing some individual shoes, the greatest number of matching pairs she could have left is *... |
orca_math | When five is added to three more than a certain number, the result is 19. What is the number? | First, I need to identify the unknown number, which I'll call "x."
The problem states that when five is added to three more than this number, the result is 19. This can be written as the equation:
5 + (x + 3) = 19
Next, I'll simplify the equation by combining like terms:
x + 8 = 19
To solve for x, I'll subtract 8 fr... | Let's solve the problem step by step.
**Problem Statement:**
When five is added to three more than a certain number, the result is 19. What is the number?
**Solution:**
1. **Let the certain number be \( x \).**
2. **Three more than the number:**
\[
x + 3
\]
3. **Five added to three more than the number:**... |
orca_math | Mrs. Wong had 30 Valentines. She gave 8 Valentines to her children, 5 Valentines to her neighbors, and 3 Valentines to her coworkers. How many Valentines does she have left? | First, I need to determine the total number of Valentines Mrs. Wong gave away. She gave 8 Valentines to her children, 5 to her neighbors, and 3 to her coworkers. Adding these together, 8 plus 5 equals 13, and 13 plus 3 equals 16. So, she gave away a total of 16 Valentines.
Next, I'll subtract the total number of Valen... | **Solution:**
Mrs. Wong started with **30** Valentines. She distributed them as follows:
- **8** Valentines to her children
- **5** Valentines to her neighbors
- **3** Valentines to her coworkers
To find out how many Valentines she has left, follow these steps:
1. **Calculate the total number of Valentines given aw... |
orca_math | Tim's cat had kittens. He gave 3 to Jessica and 6 to Sara. He now has 9 kittens. How many kittens did he have to start with? | First, I need to determine how many kittens Tim gave away in total. He gave 3 kittens to Jessica and 6 kittens to Sara. Adding these together, 3 + 6 equals 9 kittens given away.
Next, I know that after giving away the kittens, Tim has 9 kittens remaining. To find out how many kittens he originally had, I add the numbe... | **Solution:**
Let's determine how many kittens Tim originally had by following these steps:
1. **Calculate the total number of kittens given away:**
- Kittens given to Jessica: \( 3 \)
- Kittens given to Sara: \( 6 \)
\[
\text{Total kittens given away} = 3 + 6 = 9
\]
2. **Determine the number ... |
synthetic_math | A hockey league has 10 teams. During the season, each of the 10 teams plays exactly four games with each of the other teams. How many total games are played in the season? | First, I need to determine how many unique pairings of teams there are in the league. Since there are 10 teams and each game involves two teams, I can calculate the number of unique pairings using the combination formula:
\[
\text{Number of pairings} = \binom{10}{2} = \frac{10 \times 9}{2} = 45
\]
Next, each pair of ... | To determine the total number of games played in the hockey league season, follow these steps:
1. **Calculate the Number of Unique Team Pairings:**
There are 10 teams in the league. Each game involves two teams. To find the number of unique pairings of teams, use the combination formula:
\[
\text{Number of ... |
orca_math | A student got 74% in math and 81% in history. The student needs to get 70% in the third subject to achieve a certain overall average. What is the desired overall average percentage? | First, I need to determine the desired overall average percentage based on the student's scores in three subjects.
The student has already achieved 74% in Math and 81% in History. The student aims to score 70% in the third subject to reach a certain overall average.
To find the overall average, I will add the scores ... | To determine the desired overall average percentage, follow these steps:
1. **List the given percentages:**
- **Math:** 74%
- **History:** 81%
- **Third Subject:** 70%
2. **Calculate the total percentage:**
\[
\text{Total Percentage} = 74\% + 81\% + 70\% = 225\%
\]
3. **Determine the overall av... |
synthetic_math | How many matches will be held during a 10-person round-robin tennis tournament where each player plays every other player exactly once? | First, identify the number of players in the tournament, which is 10.
Each player will play against every other player exactly once. This means each player will have 9 matches.
If we simply multiply the number of players by the number of matches each player has, we get 10 × 9 = 90. However, this counts each match twi... | To determine the number of matches in a 10-person round-robin tennis tournament where each player plays every other player exactly once, follow these steps:
1. **Understand the Round-Robin Format:**
- In a round-robin tournament, each participant plays against every other participant exactly once.
2. **Calculate t... |
orca_math | sheela deposits rs . 2500 in bank savings account . if this is 25 % of her monthly income . what is her monthly income in ? | First, I recognize that Sheela deposits Rs. 2500, which represents 25% of her monthly income.
To find her total monthly income, I need to determine what amount 25% corresponds to Rs. 2500.
I can set up the equation: 25% of the monthly income equals Rs. 2500.
Converting 25% to a decimal gives 0.25.
So, 0.25 multipli... | **Solution:**
Sheela deposits **Rs. 2500**, which is **25%** of her monthly income. To find her total monthly income, follow these steps:
1. **Let the monthly income be \( x \).**
2. **According to the problem:**
\[
25\% \text{ of } x = 2500
\]
3. **Convert the percentage to a decimal:**
\[
0.25 \... |
gsm8k | Every time Carl earned $0.50 he would go to the corner market and buy a candy bar. Carl's neighbor said he would pay him $0.75 every week for taking out his trash. At the end of four weeks, how many candy bars will Carl be able to buy? | Okay, so I need to figure out how many candy bars Carl can buy after four weeks. Let me break this down step by step to make sure I understand everything correctly.
First, Carl earns money by taking out his neighbor's trash. His neighbor pays him $0.75 every week for this service. So, over four weeks, Carl will earn:
... | At the end of four weeks, Carl will be able to buy **6 candy bars**. |
orca_math | Phoebe eats 1 serving and gives her dog 1 serving of peanut butter for a bedtime snack. Each jar of peanut butter has 15 servings. She needs a certain number of jars to make sure she and her dog have enough to last for a specific number of days. If she needs 4 jars, how many days will the peanut butter last? | First, I need to determine the total number of servings Phoebe and her dog consume each day. Phoebe eats 1 serving, and she gives her dog 1 serving, so together they consume 2 servings per day.
Next, I'll calculate the total number of servings available in 4 jars of peanut butter. Each jar contains 15 servings, so 4 j... | **Solution:**
1. **Determine the daily consumption:**
- Phoebe eats **1 serving** of peanut butter.
- She gives her dog **1 serving** of peanut butter.
- **Total daily consumption** = 1 serving (Phoebe) + 1 serving (Dog) = **2 servings per day**.
2. **Calculate the total number of servings in 4 jars:**
... |
orca_math | In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 20. What quotient did the student obtain by mistake? | First, I need to determine the dividend (D) using the correct divisor and quotient. Since the correct divisor is 21 and the correct quotient is 20, I can calculate D as follows:
D = 21 * 20 = 420
Next, I need to find out the mistaken quotient when the student used 12 as the divisor instead of 21. Using the same divid... | To determine the quotient the student obtained by mistake, let's follow these steps:
1. **Identify the Given Values:**
- **Correct Divisor (D₁):** 21
- **Mistaken Divisor (D₂):** 12
- **Correct Quotient (Q₁):** 20
- **Remainder (R):** 0
2. **Find the Dividend (N):**
The dividend can be calculated u... |
orca_math | A new building needed 9 windows. The builder had already installed 6 of them. It takes a certain amount of time to install each window, and it will take him 18 hours to install the rest. How long does it take to install one window? | First, I need to determine how many windows are left to install. The building requires a total of 9 windows, and the builder has already installed 6 windows.
So, the number of windows left to install is:
9 windows - 6 windows = 3 windows
Next, I know that it will take the builder 18 hours to install these remaining 3... | To determine how long it takes to install one window, follow these steps:
1. **Calculate the number of windows left to install:**
\[
\text{Total windows needed} - \text{Windows already installed} = 9 - 6 = 3 \text{ windows}
\]
2. **Determine the time required to install the remaining windows:**
It... |
gsm8k | Tom and Tim both brought 4, six-sided dice to school. How many total sides are there? | Okay, so I need to figure out how many total sides there are when Tom and Tim both bring 4 six-sided dice to school. Let me break this down step by step.
First, I know that each die has 6 sides. That's pretty straightforward. Now, Tom brought 4 dice, and Tim also brought 4 dice. So, together, they have 4 plus 4 dice. ... | To determine the total number of sides when Tom and Tim each bring 4 six-sided dice to school, follow these steps:
1. **Calculate the total number of dice:**
- Tom brings 4 dice.
- Tim brings 4 dice.
- Total dice = 4 (Tom) + 4 (Tim) = **8 dice**.
2. **Determine the number of sides per die:**
- Each die ha... |
synthetic_amc | The sum of two nonzero real numbers is $3$ times their product. What is the sum of the reciprocals of the two numbers?
A) 1
B) 2
C) 3
D) 4
E) 6 | Let the two real numbers be \( x \) and \( y \). We are given that their sum is 3 times their product, which can be written as:
\[ x + y = 3xy \]
We need to find the sum of the reciprocals of these two numbers, which is \( \frac{1}{x} + \frac{1}{y} \).
To find this, we can manipulate the given equation. First, divid... | Let the two real numbers be \( x \) and \( y \). We are given that their sum is 3 times their product, which can be written as:
\[
x + y = 3xy
\]
We need to find the sum of the reciprocals of these two numbers, which is \( \frac{1}{x} + \frac{1}{y} \).
To find this, we can manipulate the given equation. First, divid... |
orca_math | Faye and her mom were picking carrots from their garden. Faye picked 23 carrots and her mother picked some. If only 12 of the carrots were good, and they had 16 bad carrots, how many carrots did her mother pick? | First, I need to determine the total number of carrots picked by Faye and her mother. I know that there are 12 good carrots and 16 bad carrots, so the total number of carrots is 12 + 16 = 28.
Next, I know that Faye picked 23 carrots. To find out how many carrots her mother picked, I subtract the number of carrots Faye... | **Solution:**
Let's break down the problem step by step to find out how many carrots Faye's mother picked.
1. **Total Carrots Picked:**
- **Good Carrots:** 12
- **Bad Carrots:** 16
\[
\text{Total Carrots} = \text{Good Carrots} + \text{Bad Carrots} = 12 + 16 = 28
\]
2. **Carrots Picked by Faye:... |
gsm8k | After violating the group's policies, 20 members of a Facebook group were removed by the group's admin. If each member posted 50 messages per day in the group and the number of members in the group was 150 before the admin removed some, calculate the total number of messages the remaining members would send in a week. | First, determine the number of members remaining in the group after the removal:
150 members - 20 members = 130 members.
Next, calculate the total number of messages sent by the remaining members in one day:
130 members × 50 messages/member/day = 6,500 messages/day.
Finally, find the total number of messages sent in ... | **Solution:**
1. **Determine the number of remaining members:**
Initially, there were 150 members in the group. After removing 20 members:
\[
150 - 20 = 130 \text{ members}
\]
2. **Calculate the total number of messages sent by the remaining members in one day:**
Each member sends 50 messages p... |
synthetic_math | One more than the reciprocal of a certain number is $\frac{9}{4}$. What is this original number expressed as a common fraction? | First, I need to find the original number based on the given condition that one more than its reciprocal equals 9/4.
I'll start by letting the original number be x.
According to the problem, the equation can be written as:
1 + (1/x) = 9/4
To isolate the reciprocal of x, I'll subtract 1 from both sides of the equatio... | Let's solve the problem step by step.
**Problem Statement:**
One more than the reciprocal of a certain number is \(\frac{9}{4}\). What is this original number expressed as a common fraction?
**Solution:**
1. **Let the original number be \(x\).**
2. **Set up the equation based on the given condition:**
\[
1 + ... |
orca_math | The government donated tons of sand to four Cities. City A received some tons of sand, City B received 26 tons of sand, and City C received 24 1/2 tons of sand. The total for all four cities was 95 tons, and City D received 28 tons of sand. How many tons of sand did City A receive? | First, I need to determine the total amount of sand received by Cities B, C, and D.
City B received 26 tons, City C received 24.5 tons, and City D received 28 tons. Adding these together:
26 + 24.5 + 28 = 78.5 tons.
The total sand donated to all four cities is 95 tons. To find out how much City A received, I subtract... | **Solution:**
We need to determine how many tons of sand City A received. Let's break down the information provided:
- **City B:** 26 tons
- **City C:** 24.5 tons
- **City D:** 28 tons
- **Total sand donated to all four cities:** 95 tons
To find the amount received by City A, we'll subtract the amounts received by C... |
orca_math | Sara initially has 4,892.5 black marbles. Fred gives her an additional 2,337.8 black marbles. How many black marbles does Sara have now? | First, I need to determine the total number of black marbles Sara has after receiving additional marbles from Fred.
Sara initially has 4,892.5 black marbles.
Fred gives her an additional 2,337.8 black marbles.
To find the total, I will add the initial number of marbles to the additional marbles.
Adding the two quan... | To determine how many black marbles Sara has after receiving additional marbles from Fred, follow these steps:
1. **Initial Number of Marbles:**
Sara initially has:
\[
4,\!892.5 \text{ black marbles}
\]
2. **Additional Marbles Given by Fred:**
Fred gives Sara:
\[
2,\!337.8 \text{ black ma... |
synthetic_amc | How many sets of exactly four consecutive positive integers have a sum of 34?
(A) 1 (B) 2 (C) 3 (D) 4 (E) None of the above
A) 1
B) 2
C) 3
D) 4
E) None of the above | To determine how many sets of exactly four consecutive positive integers have a sum of 34, we can use the concept of arithmetic sequences.
Let the four consecutive integers be \( n, n+1, n+2, n+3 \). The sum of these integers is given by:
\[
n + (n+1) + (n+2) + (n+3) = 4n + 6
\]
We set this equal to 34:
\[
4n + 6 = 3... | To determine how many sets of exactly four consecutive positive integers have a sum of 34, we can use the concept of arithmetic sequences.
Let the four consecutive integers be \( n, n+1, n+2, n+3 \). The sum of these integers is given by:
\[
n + (n+1) + (n+2) + (n+3) = 4n + 6
\]
We set this equal to 34:
\[
4n + 6 = 34... |
olympiads | Jitka hiked a trail. After hiking 60% of the length of the trail, she had 8 km left to go. What is the length of the trail?
(A) 28 km
(B) 12.8 km
(C) 11.2 km
(D) 13 \(\frac{1}{3}\) km
(E) 20 km | Let's denote the total length of the trail by \( L \) kilometers.
Jitka has hiked 60% of the trail, so the remaining 40% of the trail is left. This remaining distance is given as 8 km. Therefore, we can set up the equation:
\[
0.40 \times L = 8
\]
To find the total length \( L \), we solve for \( L \):
\[
L = \frac... | **Solution:**
Let's denote the total length of the trail by \( L \) kilometers.
1. **Understanding the Problem:**
- Jitka has hiked **60%** of the trail.
- The remaining **40%** of the trail is **8 km**.
2. **Setting Up the Equation:**
\[
40\% \times L = 8 \text{ km}
\]
\[
0.40 \times L = 8
\... |
orca_math | Rachel makes a certain amount as a waitress in a coffee shop. In one hour, she serves 20 different people and they all leave her a $1.25 tip. She made $37 in that hour. How much does she make per hour without tips? | First, I need to determine how much Rachel earned from tips in one hour. She served 20 people, and each person left a $1.25 tip.
Next, I'll calculate the total tips by multiplying the number of people by the tip amount:
20 people * $1.25/person = $25
Rachel's total earnings for the hour were $37. To find out how much... | To determine how much Rachel makes per hour without tips, follow these steps:
1. **Calculate Total Tips:**
Rachel received a $1.25 tip from each of the 20 people she served.
\[
\text{Total Tips} = 20 \text{ people} \times \$1.25/\text{person} = \$25
\]
2. **Determine Earnings Without Tips:**
... |
orca_math | Nancy has 7 black balloons. Mary has 4 times more black balloons than Nancy. Mary have _____ black balloons now . | First, identify the number of black balloons Nancy has, which is 7.
Mary has 4 times more black balloons than Nancy. To find out how many black balloons Mary has, multiply Nancy's number of balloons by 4.
So, 7 multiplied by 4 equals 28.
Therefore, Mary has 28 black balloons. | **Solution:**
Nancy has **7** black balloons.
Mary has **4 times** more black balloons than Nancy. To find out how many black balloons Mary has, we multiply Nancy's number of balloons by 4.
\[
\text{Mary's black balloons} = 7 \times 4 = 28
\]
**Answer:** \(\boxed{28}\) |
synthetic_math | Determine the sixth term of the geometric sequence with the first term $3$ and the second term $6$. | First, I need to determine the common ratio of the geometric sequence. I can find this by dividing the second term by the first term.
Next, I'll use the common ratio to find the sixth term of the sequence. The formula for the \( k^{\text{th}} \) term of a geometric sequence is \( a_k = a \cdot r^{k-1} \), where \( a \... | To determine the sixth term of the geometric sequence with the first term \( a = 3 \) and the second term \( 6 \), follow these steps:
1. **Find the Common Ratio (\( r \))**:
The common ratio \( r \) in a geometric sequence is found by dividing the second term by the first term:
\[
r = \frac{\text{Second ... |
orca_math | Melanie had 7 dimes in her bank. Her dad gave her some dimes and her mother gave her 4 dimes. Now, Melanie has 19 dimes. How many dimes did her dad give her? | First, Melanie starts with 7 dimes.
Her mother gives her an additional 4 dimes, bringing the total to 7 + 4 = 11 dimes.
Melanie now has a total of 19 dimes.
To find out how many dimes her dad gave her, subtract the dimes she had after her mother's contribution from the total dimes she has now: 19 - 11 = 8 dimes.
Th... | Let's determine how many dimes Melanie's dad gave her step by step.
1. **Initial Amount:**
- Melanie starts with **7 dimes**.
2. **Dimes from Mother:**
- Her mother gives her **4 dimes**.
- **Total dimes after receiving from mother:**
\[
7 \text{ (initial)} + 4 \text{ (mother)} = 11 \text{ dimes}
... |
orca_math | Alex had some ounces of jelly beans. He ate 6 ounces. Then he divided the rest equally into 3 piles, and each pile weighs 10 ounces. How many ounces of jelly beans did Alex have initially? | First, determine the total weight of the jelly beans after Alex ate 6 ounces. Since he divided the remaining jelly beans into 3 piles of 10 ounces each, the total remaining weight is 3 multiplied by 10 ounces, which equals 30 ounces.
Next, add the 6 ounces that Alex ate to the remaining 30 ounces to find the initial w... | **Solution:**
Let's determine the initial amount of jelly beans Alex had.
1. **After Eating 6 Ounces:**
Alex ate 6 ounces of jelly beans. Let the initial amount of jelly beans be \( x \) ounces. Therefore, the remaining jelly beans after eating are:
\[
x - 6 \text{ ounces}
\]
2. **Dividing into 3 Equ... |
orca_math | Every week, Lucas makes 4 pieces of chocolate candy for each of his students on Monday. This upcoming Monday, 3 of Lucas' students will not be coming to class, and he will make 28 pieces of chocolate candy. How many pieces of chocolate candy did Lucas make for his class last Monday? | First, I need to determine the total number of students Lucas has. This upcoming Monday, 3 students will not be attending, and Lucas will make 28 pieces of chocolate candy. Since he makes 4 pieces per student, I can set up the equation 4 × (S - 3) = 28, where S represents the total number of students.
Next, I'll solve... | Let's determine how many pieces of chocolate candy Lucas made for his class last Monday.
**Step 1: Find the Total Number of Students**
Let \( S \) represent the total number of students Lucas has.
This upcoming Monday, 3 students will not be attending, so Lucas will be making chocolate candy for \( S - 3 \) students... |
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