How To Solve Percentage Problems

Percentage problems such as "50 is 20 percent of what number?" and "What percent of 125 is 75?" are often difficult for students. Teaching students an easy method of substitution will have them conquering percentage problems in no time.

Step 1

Write the proportion x/100 = is/of. x is the percentage (over 100 of course), "is" refers to the part, and "of" refers to the whole.

Step 2

Fill in what you know. In the question "50 is 20 percent of what number?", x=20, is=20 ("50 is"), and of=the unknown ("of what number"). Therefore, write 20/100=50/x.

Step 3

Cross multiply. You'll have a constant on one side and a number times a variable on the other side. Here, it is 20x=5,000.

Step 4

Solve for x. Here, x=5,000/20=250, which is the answer.

Step 5

Practice by solving the other problem, "What percent of 125 is 75?" First, write, x/100=is/of. In this example, x is the unknown, is=75 ("is 75"), and "of"=125 ("of 125"). Fill in what you know to get x/100=75/125. Cross multiply to get 125x=7,500. x=60, which is the percent.