How to Solve Percentage Problems

Percentage problems such as "50 is 20% of what number?" and "What percent of 125 is 75?" are often difficult for students. This article explains how to apply a simple proportion that will help you solve percentage problems with confidence.

Things You'll Need

• paper
• pen/pencil
• calculator

Instructions

1. Start by writing 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.

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.

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

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

5. Let's solve the other problem, "What percent of 125 is 75?" for practice. 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.

Tips & Warnings

• Be sure you put the numbers in the right spots in the equation, or else your answer will be incorrect.