# Solving Problems With Proportions 20% means that 20 will replace percent in our proportion. Substitute: Now we can substitute these values into our proportion.

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and how would we solve this problem: What is 20% of 45? 40% means that 40 will replace percent in our proportion.

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

Analysis: In this problem, you are being asked 8 is what percent of 20?

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.

The phrase what percent tells us that percent is the unknown quantity.

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

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

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.

## Comments Solving Problems With Proportions

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Note that in Problem 1 we did not have to cross multiply to solve the proportion. We could have used equivalent fractions instead i.e. since 20 multiplied by 5 equals 100, we get that 8 multiplied by 5 equals x, so x equals 40.…