Question
Question 1
A)The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.(1 point)
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Question 2
A)Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes.(1 point)
$$ minutes
Question 3
A)Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-liter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.(1 point)
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Question 4
A)Randi needs to mow her lawn. The mixture requires 5 gallons of gas for every 2 gallons of oil. How much oil will she need for 8 gallons of gas? Your answer should be in tenths.(1 point)
$$ gallons
Question 5
A)Laila is laying a path down for a new driveway. The store has three types of paver stones that will work for her space. She needs to know which paver is the best price. Paver 1 costs $1.49 each, and she will need twice as many as paver 2 and half as many as paver 3. Paver 2 costs $2.50 each. Paver 3 costs $0.75. Which paver will be the best buy? Your answer should be a number.(1 point)
Paver $$
A)The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.(1 point)
$$
Question 2
A)Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes.(1 point)
$$ minutes
Question 3
A)Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-liter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.(1 point)
$$$
Question 4
A)Randi needs to mow her lawn. The mixture requires 5 gallons of gas for every 2 gallons of oil. How much oil will she need for 8 gallons of gas? Your answer should be in tenths.(1 point)
$$ gallons
Question 5
A)Laila is laying a path down for a new driveway. The store has three types of paver stones that will work for her space. She needs to know which paver is the best price. Paver 1 costs $1.49 each, and she will need twice as many as paver 2 and half as many as paver 3. Paver 2 costs $2.50 each. Paver 3 costs $0.75. Which paver will be the best buy? Your answer should be a number.(1 point)
Paver $$
Answers
Answer
Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes.(1 point)
Answer
no
Answered by
GPT-4o mini
Let's solve each question one by one.
### Question 1
The ratio of girls to boys is 3:1, meaning for every 3 girls there is 1 boy.
Let the number of boys be \( b \).
Then the number of girls is \( 3b \).
The total number of students is the sum of boys and girls:
\[
b + 3b = 400
\]
\[
4b = 400
\]
\[
b = \frac{400}{4} = 100
\]
**Answer for Question 1: 100**
### Question 2
In 30 minutes, Karen reads 10 pages and completes 15 math problems.
To find out how long it will take her to read 30 pages and complete 45 math problems:
- Time to read 30 pages:
\[
\text{If she reads 10 pages in 30 minutes, then for 30 pages, it will take } \frac{30}{10} \times 30 = 90 \text{ minutes.}
\]
- Time to complete 45 math problems:
\[
\text{If she does 15 problems in 30 minutes, then for 45 problems, it will take } \frac{45}{15} \times 30 = 90 \text{ minutes.}
\]
Total time:
\[
90 + 90 = 180 \text{ minutes.}
\]
**Answer for Question 2: 180 minutes**
### Question 3
To make the punch:
- 1 gallon of sorbet = 4 quarts. Therefore, he pays $4.00 for 1 quart of sorbet, which means he pays \( 4.00 \times 4 = 16.00 \) for a gallon.
- Cost of 2 liters of lemon-lime soda = $3.00.
Total cost:
\[
16.00 + 3.00 = 19.00
\]
He wants to make a profit of $10. Therefore:
\[
\text{Total Revenue} = \text{Total Cost} + \text{Profit} = 19.00 + 10.00 = 29.00
\]
He makes 12 cups of punch, so the price per cup:
\[
\text{Price per cup} = \frac{29.00}{12} \approx 2.41667
\]
Rounded to the nearest hundredth, this is $2.42.
**Answer for Question 3: 2.42**
### Question 4
The mixture requires 5 gallons of gas for every 2 gallons of oil. To find out how much oil Randi needs for 8 gallons of gas:
Using the ratio of gas to oil (5 gallons gas required 2 gallons oil):
\[
\text{Proportion} = \frac{2}{5}
\]
For 8 gallons of gas:
\[
\text{oil needed} = 8 \times \frac{2}{5} = \frac{16}{5} = 3.2 \text{ gallons.}
\]
**Answer for Question 4: 3.2 gallons**
### Question 5
Let \( n \) be the number of paver stones needed for paver 2, priced at $2.50 each.
- Paver 1: Needs \( 2n \) stones, costing \( 1.49 \times 2n = 2.98n \).
- Paver 3: Needs \( \frac{n}{2} \) stones, costing \( 0.75 \times \frac{n}{2} = 0.375n \).
Now we will express the total costs for all three:
- Cost for Paver 1: \( 2.98n \)
- Cost for Paver 2: \( 2.50n \)
- Cost for Paver 3: \( 0.375n \)
Now to compare:
1. Paver 1: \( 2.98n \)
2. Paver 2: \( 2.50n \)
3. Paver 3: \( 0.375n \)
To find the best price, just compare the total costs per paver by assuming \( n = 1 \) (since it will scale with the number of stones):
- Paver 1: $2.98
- Paver 2: $2.50
- Paver 3: $0.375
Paver 3 is the cheapest at $0.375 per stone.
**Answer for Question 5: Paver 3**
### Question 1
The ratio of girls to boys is 3:1, meaning for every 3 girls there is 1 boy.
Let the number of boys be \( b \).
Then the number of girls is \( 3b \).
The total number of students is the sum of boys and girls:
\[
b + 3b = 400
\]
\[
4b = 400
\]
\[
b = \frac{400}{4} = 100
\]
**Answer for Question 1: 100**
### Question 2
In 30 minutes, Karen reads 10 pages and completes 15 math problems.
To find out how long it will take her to read 30 pages and complete 45 math problems:
- Time to read 30 pages:
\[
\text{If she reads 10 pages in 30 minutes, then for 30 pages, it will take } \frac{30}{10} \times 30 = 90 \text{ minutes.}
\]
- Time to complete 45 math problems:
\[
\text{If she does 15 problems in 30 minutes, then for 45 problems, it will take } \frac{45}{15} \times 30 = 90 \text{ minutes.}
\]
Total time:
\[
90 + 90 = 180 \text{ minutes.}
\]
**Answer for Question 2: 180 minutes**
### Question 3
To make the punch:
- 1 gallon of sorbet = 4 quarts. Therefore, he pays $4.00 for 1 quart of sorbet, which means he pays \( 4.00 \times 4 = 16.00 \) for a gallon.
- Cost of 2 liters of lemon-lime soda = $3.00.
Total cost:
\[
16.00 + 3.00 = 19.00
\]
He wants to make a profit of $10. Therefore:
\[
\text{Total Revenue} = \text{Total Cost} + \text{Profit} = 19.00 + 10.00 = 29.00
\]
He makes 12 cups of punch, so the price per cup:
\[
\text{Price per cup} = \frac{29.00}{12} \approx 2.41667
\]
Rounded to the nearest hundredth, this is $2.42.
**Answer for Question 3: 2.42**
### Question 4
The mixture requires 5 gallons of gas for every 2 gallons of oil. To find out how much oil Randi needs for 8 gallons of gas:
Using the ratio of gas to oil (5 gallons gas required 2 gallons oil):
\[
\text{Proportion} = \frac{2}{5}
\]
For 8 gallons of gas:
\[
\text{oil needed} = 8 \times \frac{2}{5} = \frac{16}{5} = 3.2 \text{ gallons.}
\]
**Answer for Question 4: 3.2 gallons**
### Question 5
Let \( n \) be the number of paver stones needed for paver 2, priced at $2.50 each.
- Paver 1: Needs \( 2n \) stones, costing \( 1.49 \times 2n = 2.98n \).
- Paver 3: Needs \( \frac{n}{2} \) stones, costing \( 0.75 \times \frac{n}{2} = 0.375n \).
Now we will express the total costs for all three:
- Cost for Paver 1: \( 2.98n \)
- Cost for Paver 2: \( 2.50n \)
- Cost for Paver 3: \( 0.375n \)
Now to compare:
1. Paver 1: \( 2.98n \)
2. Paver 2: \( 2.50n \)
3. Paver 3: \( 0.375n \)
To find the best price, just compare the total costs per paver by assuming \( n = 1 \) (since it will scale with the number of stones):
- Paver 1: $2.98
- Paver 2: $2.50
- Paver 3: $0.375
Paver 3 is the cheapest at $0.375 per stone.
**Answer for Question 5: Paver 3**
Answered by
GPT-4o mini
To determine how long it will take Karen to do her homework, we need to calculate the time for both reading and math problems separately.
### Reading Time
Karen can read 10 pages in 30 minutes. To find out how long it will take her to read 30 pages, we can set up a proportion:
\[
\text{Time to read 30 pages} = \left(\frac{30 \text{ pages}}{10 \text{ pages}}\right) \times 30 \text{ minutes} = 3 \times 30 \text{ minutes} = 90 \text{ minutes}.
\]
### Math Problem Time
Karen can complete 15 math problems in 30 minutes. To find out how long it will take her to complete 45 math problems, we can set up a similar proportion:
\[
\text{Time to complete 45 problems} = \left(\frac{45 \text{ problems}}{15 \text{ problems}}\right) \times 30 \text{ minutes} = 3 \times 30 \text{ minutes} = 90 \text{ minutes}.
\]
### Total Time
Now, we add both times together to find the total time required for Karen:
\[
\text{Total time} = \text{Time to read} + \text{Time to complete problems} = 90 \text{ minutes} + 90 \text{ minutes} = 180 \text{ minutes}.
\]
Therefore, it will take Karen a total of **180 minutes** to complete her homework.
**Answer: 180 minutes**
### Reading Time
Karen can read 10 pages in 30 minutes. To find out how long it will take her to read 30 pages, we can set up a proportion:
\[
\text{Time to read 30 pages} = \left(\frac{30 \text{ pages}}{10 \text{ pages}}\right) \times 30 \text{ minutes} = 3 \times 30 \text{ minutes} = 90 \text{ minutes}.
\]
### Math Problem Time
Karen can complete 15 math problems in 30 minutes. To find out how long it will take her to complete 45 math problems, we can set up a similar proportion:
\[
\text{Time to complete 45 problems} = \left(\frac{45 \text{ problems}}{15 \text{ problems}}\right) \times 30 \text{ minutes} = 3 \times 30 \text{ minutes} = 90 \text{ minutes}.
\]
### Total Time
Now, we add both times together to find the total time required for Karen:
\[
\text{Total time} = \text{Time to read} + \text{Time to complete problems} = 90 \text{ minutes} + 90 \text{ minutes} = 180 \text{ minutes}.
\]
Therefore, it will take Karen a total of **180 minutes** to complete her homework.
**Answer: 180 minutes**
Answered by
GPT-4o mini
Let's go through the calculations step by step once more to clearly determine how much time Karen will need to complete her tasks.
### Given Information:
- Karen reads 10 pages in 30 minutes.
- Karen completes 15 math problems in 30 minutes.
### Required Tasks:
- Read 30 pages.
- Complete 45 math problems.
### Step 1: Calculate the Reading Time
Karen reads 10 pages in 30 minutes, so we can find her reading rate:
- **Rate of reading**: \( \frac{10 \text{ pages}}{30 \text{ minutes}} = \frac{1 \text{ page}}{3 \text{ minutes}} \)
To read 30 pages:
\[
\text{Time to read 30 pages} = 30 \text{ pages} \times 3 \text{ minutes per page} = 90 \text{ minutes}
\]
### Step 2: Calculate the Math Problem Completion Time
Karen completes 15 math problems in 30 minutes, so we can find her completion rate:
- **Rate of completing problems**: \( \frac{15 \text{ problems}}{30 \text{ minutes}} = \frac{1 \text{ problem}}{2 \text{ minutes}} \)
To complete 45 problems:
\[
\text{Time to complete 45 problems} = 45 \text{ problems} \times 2 \text{ minutes per problem} = 90 \text{ minutes}
\]
### Step 3: Total Time Calculation
Now, we add the time for reading and completing math problems:
\[
\text{Total time} = \text{Time to read} + \text{Time to complete problems} = 90 \text{ minutes} + 90 \text{ minutes} = 180 \text{ minutes}
\]
Thus, the total amount of time Karen will need to do her homework is **180 minutes**.
If this is still not the answer you were expecting, please clarify what part is incorrect, and I'll be happy to assist further!
### Given Information:
- Karen reads 10 pages in 30 minutes.
- Karen completes 15 math problems in 30 minutes.
### Required Tasks:
- Read 30 pages.
- Complete 45 math problems.
### Step 1: Calculate the Reading Time
Karen reads 10 pages in 30 minutes, so we can find her reading rate:
- **Rate of reading**: \( \frac{10 \text{ pages}}{30 \text{ minutes}} = \frac{1 \text{ page}}{3 \text{ minutes}} \)
To read 30 pages:
\[
\text{Time to read 30 pages} = 30 \text{ pages} \times 3 \text{ minutes per page} = 90 \text{ minutes}
\]
### Step 2: Calculate the Math Problem Completion Time
Karen completes 15 math problems in 30 minutes, so we can find her completion rate:
- **Rate of completing problems**: \( \frac{15 \text{ problems}}{30 \text{ minutes}} = \frac{1 \text{ problem}}{2 \text{ minutes}} \)
To complete 45 problems:
\[
\text{Time to complete 45 problems} = 45 \text{ problems} \times 2 \text{ minutes per problem} = 90 \text{ minutes}
\]
### Step 3: Total Time Calculation
Now, we add the time for reading and completing math problems:
\[
\text{Total time} = \text{Time to read} + \text{Time to complete problems} = 90 \text{ minutes} + 90 \text{ minutes} = 180 \text{ minutes}
\]
Thus, the total amount of time Karen will need to do her homework is **180 minutes**.
If this is still not the answer you were expecting, please clarify what part is incorrect, and I'll be happy to assist further!
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