# Solving Proportion Problems Identify: 18 is the part and will replace IS in our proportion.75% means that 75 will replace PERCENT in our proportion.But how would we solve this problem: 18 is 40% of what number? Identify: The phrase 18 is means that 18 is the part.

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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?

In Problem 1 we let x represent the unknown quantity "what percent"; in Problem 2 we let x represent the unknown quantity "of what number"; and in Problem 3 we let x represent the unknown quantity "What is." Thus, we solved three different percent problems, where in each problem, two numbers were given and we were asked to find the third.

We did this by letting a variable represent the unknown quantity and then substituting the given values into a proportion to solve for the unknown quantity.

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

## Solving Proportion Problems

We will let variable x represent this unknown quantity in our proportion.You are given two numbers from the proportion above and asked to find the third.The percent is the unknown quantity in this problem. Identify: The phrase 8 is means that 8 is the part.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.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.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.

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