ACT Math : How to find proportion
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Example Questions
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 #52 : 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?
60
120
10
30
100
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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