Solving Proportion Problems

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The phrase of what number represents the whole and is the unknown quantity.

We will let variable x represent this unknown quantity in our proportion.

PERCENT is the unknown quantity in our proportion, to be represented by n.

Substitute: becomes Solve: Cross multiply and we get: 56n = 14(100), or 56n = 1400 Divide both sides by 56 and we get: n = 25 Solution: 25% of 56 is 14 Problem 6: 18 is 75% of what number?

Substitute: Now we can substitute these values into our proportion.

becomes Solve: Cross multiply and we get: 40x = 18(100) or 40x = 1800 Divide both sides by 40 to solve for x and we get: x = 45 Solution: 18 is 40% of 45 Problem 3: What is 20% of 45?The phrase what percent tells us that percent is the unknown quantity.This unknown quantity will be represented by x in our proportion. Substitute: Now we can substitute these values into our proportion.Identify: 18 is the part and will replace IS in our proportion.75% means that 75 will replace PERCENT in our proportion.becomes Solve: Cross multiply and we get: 100x = 45(20) or 100x = 900 Divide both sides by 100 to solve for x and we get: x = 9 Solution: 9 is 20% of 45 In Problems 1, 2 and 3 we are given two numbers and asked to find the third by using a proportion.However, the unknown quantity was different for each problem. Red is used for the unknown quantity in each problem.But what would you do if you given this problem: 8 is what percent of 20?In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.In previous lessons, you were shown how to convert a decimal to a percent and a percent to a decimal.Thus, if you were asked to Find 15% of 120, you would multiply .15 by 120, to get an answer of 18.

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