In this section we will solve each percentage problem using two different methods.
After you try the two methods, take your pick of which one works best for you. It’s your call, boss.
Method 1: Using Ratios and Proportions
All percent problems can be set up as proportions. The tricky part is figuring out what goes where in the proportion. Here are a few things to know when setting it up:
 A percent is a proportion where the whole is equal to 100. "Per" means "of" and "cent" is a Latin prefix meaning "hundred." Think of the words century (100 years) and centimeter (onehundredth of a meter).
 You are looking for a percentage of the number that will become the denominator of the ratio. An easy way to think about this is that whatever comes after the "of" is the denominator.
 The word "what" represents the thing you are trying to find, so "what" is our variable.
Take a look at Examples 14 to see how Method 1 works.
Method 2: Using Equations
Each of these problems can also be set up as equations. All you have to do is "translate" the sentences. Here is what you have to remember:
 What means the variable, x
 Is means equals
 Of means to multiply
 Write all percents as decimals in your equation.
Check out the 5th 8th Examples below to see how Method 2 works.
Working With Percents Practice:
What is 15% of 72?  
 Our first proportion is the percentage. 15% means 15 out of 100. 
 We want to find 15% of 72, so 72 is a denominator. Solve for x. Cross multiply. 
 Divide by the coefficient of x. 
 So 15% of 72 is 10.8 
80% of 40 is what number?  
 Our first proportion is the percentage. 80% means 80 out of 100. 
 We need to find 80% of 40, so 40 is a denominator. Solve for x. Cross multiply. 
 Divide by the coefficient of x. 
 So 80% of 40 is 32 
30% of what number is 15?  
 Our first proportion is the percentage. 30% means 30 out of 100. 
 We need to find 30% of a number, x, so x is a denominator. Solve for x. Cross multiply. 
 Divide by the coefficient of x. 
 So 30% of 50 is 15 
What percent of 60 is 20?  
 Our first proportion is the percentage. We do not know our %, so it is x. 
 20 is part of 60, so that is a ratio of 20/60. Solve for x. Cross multiply. 
 Divide by the coefficient of x. 
 
What is 15% of 72? 

 Write 15% as a decimal. 
 Translate the equation. What (x) is (=) 15% of (multiply) 72? 
 Solve the equation. It’s 10.8 
80% of 40 is what number?  
 Write 80% as a decimal. 
 Translate the equation. 80% of (multiply) 40 is (=) what number (x)? 
 Solve the equation. It’s 32. 
30% of what number is 15?  
 Write 30% as a decimal. 
 Translate the equation. 30% of (multiply) what number (x) is (=)15? 
 Solve the equation; divide by the coefficient. 
 It’s 50 
What percent of 60 is 20?  
 Here our percentage is unknown, so it is x. 
 Translate the equation. What percent (x) of (multiply) 60 is (=) 20? 
 Solve the equation; divide by the coefficient. 
 Reduce the fraction 
 Finally, translate this back into a percent. 
45% of what number is 202.5?
Hint
60 is what percent of 110?
Hint
Answer
250% of 40 is what number?