How to find proportion - ACT Math
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In a school relay race, every 5-man team must sprint 110 yards total. However, Jim’s team is short a person. Thus, Jim must run two sections for his team. How far does Jim have to run?
In a school relay race, every 5-man team must sprint 110 yards total. However, Jim’s team is short a person. Thus, Jim must run two sections for his team. How far does Jim have to run?
We first find out how much each person must run. Thus we take 110/5 to get 22 yards. However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.
We first find out how much each person must run. Thus we take 110/5 to get 22 yards. However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.
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A building that is 30 feet tall casts a shadow that is 50 feet long. If another building casts a shadow that is 100 feet long, how tall is the building?
A building that is 30 feet tall casts a shadow that is 50 feet long. If another building casts a shadow that is 100 feet long, how tall is the building?
This problem can be set up as a proportion: 30 feet/x feet = 50 feet/100 feet. To solve, we simply cross multiply: (30 feet * 100 feet) = (50 feet * x feet). Thus, 3000 feet = 50_x_ feet. To solve for x, divide each side by 50. Therefore, x = 60 feet. If you got 167 feet, you may have set up the proportion incorrectly by mixing up the height of the building with the length of the shadow. If you got 6 feet or 600 feet, you may have made a computational error. If you got 1670 feet, you may have set the proportion up incorrectly and made a computational error.
This problem can be set up as a proportion: 30 feet/x feet = 50 feet/100 feet. To solve, we simply cross multiply: (30 feet * 100 feet) = (50 feet * x feet). Thus, 3000 feet = 50_x_ feet. To solve for x, divide each side by 50. Therefore, x = 60 feet. If you got 167 feet, you may have set up the proportion incorrectly by mixing up the height of the building with the length of the shadow. If you got 6 feet or 600 feet, you may have made a computational error. If you got 1670 feet, you may have set the proportion up incorrectly and made a computational error.
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If a bicyclist can bike 24 miles per hour, how far (in miles) can he travel in 2 minutes, assuming he bikes at a constant speed (answer rounded to the nearest tenth)?
If a bicyclist can bike 24 miles per hour, how far (in miles) can he travel in 2 minutes, assuming he bikes at a constant speed (answer rounded to the nearest tenth)?
0.8 mile. Using some conversions: ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile
0.8 mile. Using some conversions: ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile
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If 10,000 lbs of cement makes 85,000 lbs of concrete, how many pounds of concrete can be made with 3,000 pounds of cement?
If 10,000 lbs of cement makes 85,000 lbs of concrete, how many pounds of concrete can be made with 3,000 pounds of cement?
25,500 lbs of concrete. Setting up a ratio with x representing the number of pounds concrete the 3,000 of cement produces, we obtain the relation: (10,000/85,000) = (3,000/x), x = 25,500 pounds of concrete.
25,500 lbs of concrete. Setting up a ratio with x representing the number of pounds concrete the 3,000 of cement produces, we obtain the relation: (10,000/85,000) = (3,000/x), x = 25,500 pounds of concrete.
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A group of 15 friends is having lunch together. Each person eats at least 2/3 of a pizza. What is the smallest number of whole pizzas needed for lunch?
A group of 15 friends is having lunch together. Each person eats at least 2/3 of a pizza. What is the smallest number of whole pizzas needed for lunch?
The minimum number of whole pizzas needed is 15(2/3) = 10.
The minimum number of whole pizzas needed is 15(2/3) = 10.
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There are 150 students in a lecture hall class in college. 12% of the students received an A. 20 students received a B. Twice the number of students who earned an A received a C. The remainder of the students received a D. Which grade did the students receive more than any other?
There are 150 students in a lecture hall class in college. 12% of the students received an A. 20 students received a B. Twice the number of students who earned an A received a C. The remainder of the students received a D. Which grade did the students receive more than any other?
First find 12% of 150, so 0.12 * 150 = 18 students received an A.
20 students received a B, and 36 students received a C (double the A's).
To find the number of D-grades, all we have to do is subtract these from the total (since there were no grades of F),
Thus: 150 – 18 – 20 – 36 = 76 students who received a D in the course, which is the most common grade.
First find 12% of 150, so 0.12 * 150 = 18 students received an A.
20 students received a B, and 36 students received a C (double the A's).
To find the number of D-grades, all we have to do is subtract these from the total (since there were no grades of F),
Thus: 150 – 18 – 20 – 36 = 76 students who received a D in the course, which is the most common grade.
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A brownie recipes calls for a 1:5 ratio of water to brownie mix. If you need 90 cups of brownie mix, how much water do you need?
A brownie recipes calls for a 1:5 ratio of water to brownie mix. If you need 90 cups of brownie mix, how much water do you need?
First set up a proportion, 1/5 = x/90, then solve for x: 5x = 90 → x = 18 cups.
First set up a proportion, 1/5 = x/90, then solve for x: 5x = 90 → x = 18 cups.
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If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?
If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?
A proportion is a statement of equality between two fractions or two ratios. Set up a proportion between the size of the drink and the calories. To solve a proportion cross multiply and solve the resulting equation.
75/12 = x/8 → 150/24 = 3x/24 → 50/8 = x/8 → x = 50
A proportion is a statement of equality between two fractions or two ratios. Set up a proportion between the size of the drink and the calories. To solve a proportion cross multiply and solve the resulting equation.
75/12 = x/8 → 150/24 = 3x/24 → 50/8 = x/8 → x = 50
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The ratio of the length of 
to the length of 
is 7:5. 
is 35 units long. How long is 
?
The ratio of the length of 
First, let's set up a proportion. We know that the ratio of 
to 
is 7 to 5. We also know that 
is 35; therefore, our proportion will look like the following:
Let's cross multiply to arrive at the following expression:
The length of 
is equal to 25.
First, let's set up a proportion. We know that the ratio of 
Let's cross multiply to arrive at the following expression:
The length of 
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A hospital that is 20 feet tall is currently casting a daytime shadow that is 10 feet long. A courthouse that is 60 feet tall is next to the hospital. How long, in feet, is the shadow cast by the courthouse?
A hospital that is 20 feet tall is currently casting a daytime shadow that is 10 feet long. A courthouse that is 60 feet tall is next to the hospital. How long, in feet, is the shadow cast by the courthouse?
In order to solve this question, set up a ratio between the height of the building and the shadow it casts.
Substitute the known values.
Cross multiply and solve for the variable.
In order to solve this question, set up a ratio between the height of the building and the shadow it casts.
Substitute the known values.
Cross multiply and solve for the variable.
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Max will be age X in 5 years. How old was he 4 years ago?
Max will be age X in 5 years. How old was he 4 years ago?
Max will be X in 5 years. So today he is X -5 and 4 years ago he was (X-5) - 4, that is X – 9. It always helps to put numbers into the equations. Example: Max will be 12 in 5 years. How old was he 4 years ago? So today Max is 12 – 5 = 7. Therefore, four years ago he was 7 -4 =3. Which is 12-5-4 =12-9 = 3
Max will be X in 5 years. So today he is X -5 and 4 years ago he was (X-5) - 4, that is X – 9. It always helps to put numbers into the equations. Example: Max will be 12 in 5 years. How old was he 4 years ago? So today Max is 12 – 5 = 7. Therefore, four years ago he was 7 -4 =3. Which is 12-5-4 =12-9 = 3
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If a pizza pie that has 16 slices and costs $12.00 is to be shared among 8 friends, how much should each person contribute?
If a pizza pie that has 16 slices and costs $12.00 is to be shared among 8 friends, how much should each person contribute?
It is $12 divided by 8 which is $1.50. The number of slices in the pizza pie is not relevant in this question.
It is $12 divided by 8 which is $1.50. The number of slices in the pizza pie is not relevant in this question.
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The largest of three numbers is six less than four times the smallest number. The middle number is three more than twice the smallest number. The sum of twice the largest number, three more than three times the middle number, and four times the smallest number is 90. What is the value of the largest number?
The largest of three numbers is six less than four times the smallest number. The middle number is three more than twice the smallest number. The sum of twice the largest number, three more than three times the middle number, and four times the smallest number is 90. What is the value of the largest number?
Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.
2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5
4(6)-6 = 14
Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.
2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5
4(6)-6 = 14
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If there are 75 calories in a 6 oz glass of juice, how many calories will there be in an 8 oz glass?
If there are 75 calories in a 6 oz glass of juice, how many calories will there be in an 8 oz glass?
We set up a proportion:
where 
= calories.
We cross multiply to get 
, so there will be 100 calories in 8 oz of juice.
We set up a proportion:
We cross multiply to get
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Tom, Tim, and Tammy ate an entire cake in the ratio of 
, respectively. If the cake had nine pieces, how many pieces did Tim eat?
Tom, Tim, and Tammy ate an entire cake in the ratio of
For ratio problems, we want to sum the total numbers in the ratio to create a fraction. 
equal portions. Therefore, the fraction of the cake that Tim eats is simply 
This, we need to multiply by the total number of pieces in the cake to find how many pieces he ate: 
For ratio problems, we want to sum the total numbers in the ratio to create a fraction.
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