ACT Math : Proportion / Ratio / Rate
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Example Questions
Example Question #1 : How To Find Proportion
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?
The students who got B's
The students who got D's.
The students who got C's
The students who got A's.
Cannot be determined.
The students who got D's.
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.
Example Question #91 : Fractions
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?
6 cups
18 cups
36 cups
25 cups
450 cups
18 cups
First set up a proportion, 1/5 = x/90, then solve for x: 5x = 90 → x = 18 cups.
Example Question #51 : Proportion / Ratio / Rate
If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?
70
50
55
60
65
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
Example Question #1 : How To Find Proportion
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:
We cross multiply to get 
Example Question #51 : Proportion / Ratio / Rate
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?
18
14
22
12
10
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
Example Question #52 : Proportion / Ratio / Rate
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?
7
10
15
5
10
The minimum number of whole pizzas needed is 15(2/3) = 10.
Example Question #421 : Arithmetic
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. 
Example Question #51 : Proportion / Ratio / Rate
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?
10
30
100
120
60
30
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.
Example Question #51 : Proportion / Ratio / Rate
The ratio of the length of 
20
5
15
25
30
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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