Solve Mixture Problems with Proportions Practice 23-24 Math 7 A, 6.23 / Use Proportional Relationships
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
(even though this is for the practice, I'll put the quick check answers here because math makes us all cry)
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1. 50 students
2. 50 minutes
3. 0.5 cup
4. 28 cups
5. 3 tsp
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hope this helps :D
-Sad-girl :)
To solve this problem, we can set up a proportion to find the number of boys in the school.
The ratio of girls to boys is given as 3 to 1. This means that for every 3 girls, there is 1 boy.
Let B represent the number of boys in the school.
Thus, we have the following proportion:
3 girls / 1 boy = (400 - B) girls / B boys
Now, we can cross-multiply and solve for B:
3B = 400 - B
4B = 400
B = 400 / 4
B = 100
Therefore, there are 100 boys in the school.
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
First, we need to determine the rate at which Karen can read pages and complete math problems in 30 minutes.
We can set up a proportion using the rate:
10 pages / 15 math problems = 30 minutes / X
To find the time it takes for Karen to do her homework, we can set up another proportion:
30 pages / 45 math problems = X minutes / 1
Now, we can cross-multiply and solve for X:
10 / 15 = 30 / X
To find X, we divide both sides of the equation by (10/15):
X = (30 * 15) / 10
X = 45
Therefore, it will take Karen 45 minutes to complete her homework.
wrong
Apologies for the mistake. Let's correct it:
We can set up a proportion using the rate:
10 pages / 15 math problems = 30 minutes / X
To find the time it takes for Karen to do her homework, we can set up another proportion:
30 pages / 45 math problems = X minutes / 1
Now, we can cross-multiply and solve for X:
10 * X = 15 * 30
10X = 450
X = 450 / 10
X = 45
Therefore, it will take Karen 45 minutes to complete her homework with 30 pages to read and 45 math problems to complete.
45 is wrong
Apologies once again for the mistake. Let's correct it:
To solve this problem, we need to find the time it takes for Karen to complete her homework when she has 30 pages to read and 45 math problems to complete.
From the given information, we know that Karen can read 10 pages and complete 15 math problems in 30 minutes. This means that her rate of reading pages and completing math problems is constant.
Let's determine Karen's rate:
Rate of reading pages = 10 pages / 30 minutes = 1/3 pages per minute
Rate of completing math problems = 15 problems / 30 minutes = 1/2 problems per minute
Now, we can calculate the time it takes for Karen to do her homework:
Time to read 30 pages = (30 pages) / (1/3 pages per minute) = 90 minutes
Time to complete 45 math problems = (45 problems) / (1/2 problems per minute) = 90 minutes
Therefore, it will take Karen 90 minutes to complete her homework with 30 pages to read and 45 math problems to complete.
yay that is correct
I'm glad the answer is correct! If you have any more questions or need further assistance, feel free to ask.
Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of Sprite to make 12 cups. He pays $3.00 for a 2-liter container of Sprite 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.
plz answer correct
To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to calculate the total cost and then add the desired profit to it.
1 gallon of sorbet is equal to 4 quarts, and Rafael needs a gallon of sorbet. So the cost of sorbet is: 4 quarts * $4.00/quart = $16.00
2 liters of Sprite are required, and Rafael pays $3.00 for a 2-liter container of Sprite.
To convert the liters to gallons, we need to divide by the conversion factor of 3.78541 liters per gallon:
2 liters / 3.78541 = 0.5283 gallons
Hence, the cost of Sprite is: 0.5283 gallons * $3.00/gallon = $1.58
Therefore, the total cost is: $16.00 + $1.58 = $17.58
Now let's calculate the cost per cup of punch:
12 cups * 1/12 gallon (since 1 gallon is required to make 12 cups) = 1 gallon
To calculate the minimum amount Rafael should charge per cup to make a $10 profit, we can use the formula:
Minimum cost per cup = (Total cost + Desired profit) / Number of cups
Minimum cost per cup = ($17.58 + $10.00) / 12 = $1.46
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $1.46 (rounded to the nearest hundredth).
that is incorrect
Apologies for the mistake. Let's correct it:
To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to calculate the total cost and then add the desired profit to it.
1 gallon of sorbet is equal to 4 quarts, and Rafael needs a gallon of sorbet. So the cost of sorbet is: 4 quarts * $4.00/quart = $16.00
2 liters of Sprite are required, and Rafael pays $3.00 for a 2-liter container of Sprite.
To convert the liters to gallons, we need to divide by the conversion factor of 3.78541 liters per gallon:
2 liters / 3.78541 = 0.5283 gallons
Hence, the cost of Sprite is: 0.5283 gallons * $3.00/gallon = $1.585
Therefore, the total cost is: $16.00 + $1.585 = $17.585 (rounded to the nearest cent)
Now let's calculate the cost per cup of punch:
12 cups * 1/12 gallon (since 1 gallon is required to make 12 cups) = 1 gallon
To calculate the minimum amount Rafael should charge per cup to make a $10 profit, we can use the formula:
Minimum cost per cup = (Total cost + Desired profit) / Number of cups
Minimum cost per cup = ($17.585 + $10.00) / 12 = $2.649 (rounded to the nearest cent)
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.65 (rounded to the nearest hundredth).
sorry but that is wrong to
Apologies for the incorrect response. Let's correct it:
To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to calculate the total cost and then add the desired profit to it.
1 gallon of sorbet is equal to 4 quarts, and Rafael needs a gallon of sorbet. So the cost of sorbet is: 4 quarts * $4.00/quart = $16.00
2 liters of Sprite are required, and Rafael pays $3.00 for a 2-liter container of Sprite.
To convert the liters to gallons, we need to divide by the conversion factor of 3.78541 liters per gallon:
2 liters / 3.78541 = 0.5283 gallons
Hence, the cost of Sprite is: 0.5283 gallons * $3.00/gallon = $1.585 (rounded to the nearest cent)
Therefore, the total cost is: $16.00 + $1.585 = $17.585 (rounded to the nearest cent)
Now let's calculate the cost per cup of punch:
12 cups * 1 gallon (since 1 gallon is required to make 12 cups) = 12 gallons
To calculate the minimum amount Rafael should charge per cup to make a $10 profit, we can use the formula:
Minimum cost per cup = (Total cost + Desired profit) / Number of cups
Minimum cost per cup = ($17.585 + $10.00) / 12 = $2.9654 (rounded to the nearest cent)
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.97 (rounded to the nearest hundredth).
incorrect as well
Apologies for the previous incorrect responses. Let's correct it:
To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to calculate the total cost and then add the desired profit to it.
1 gallon of sorbet is equal to 4 quarts, and Rafael needs a gallon of sorbet. So the cost of sorbet is: 4 quarts * $4.00/quart = $16.00.
2 liters of Sprite are required, and Rafael pays $3.00 for a 2-liter container of Sprite.
To convert the liters to gallons, we need to divide by the conversion factor of 3.78541 liters per gallon:
2 liters / 3.78541 = 0.5283 gallons
Hence, the cost of Sprite is: 0.5283 gallons * $3.00/gallon = $1.585 (rounded to the nearest cent).
Therefore, the total cost is: $16.00 + $1.585 = $17.585 (rounded to the nearest cent).
Now let's calculate the cost per cup of punch:
To make 12 cups of punch, Rafael needs a total of 12 cups / 16 cups per gallon = 0.75 gallons.
To calculate the minimum amount Rafael should charge per cup to make a $10 profit, we can use the formula:
Minimum cost per cup = (Total cost + Desired profit) / Number of cups
Minimum cost per cup = ($17.585 + $10.00) / (12 cups * 0.75) = $3.80 (rounded to the nearest cent).
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $3.80 (rounded to the nearest hundredth).