How to Solve a Proportion With a Variable in It

Proportions are ratios that are set equal to each other. The ratios will usually be in fraction form. The easiest way to determine if the ratios are equal is to cross multiply the denominators by the numerators. The products of both formulas should be equal. When a proportional ratio has an unknown value, like those asked for in most proportional word problems, a variable, or letter will represent that unknown value throughout the proportion equation and solution process. After the fractions are broken down to a simplified formula, the variable is isolated on one side of the equation, with its value on the other side.

Instructions

1. Solve the word problem: It takes 15 minutes to burn 6 CDs. How long will it take to burn 10 CDs?

2. Write a a proportion that equates the two ratios. Fifteen minutes to 6 CDs equals an unknown number of minutes to burn 10 CDs.

3. Simplify the ratios to numeric form, using the variable x to represent the unknown number of minutes. 15/6 = x/10. Notice that the number of minutes is in the numerator for both ratios.

4. Cross-multiply the numerators by the denominator: 15 x 10 = 150 and 6 x (x) = 6x. Simplify the formula: 150 = 6x.

5. Divide both sides of the formula by the coefficient of the variable: 150 ÷ 6 = 25 and 6x ÷ 6 = x. Simplify for the solution: x = 25. Therefore it will take 25 minutes to burn 10 CDs.

6. Plug the value of the variable back into the formula: 15/6 = 25/10. Cross multiply to check if the proportions are equal: 15 x 10 = 150 and 25 x 6 = 150.

Tips & Warnings

• When setting up a proportion equation, the same unit of measurement should go into the same location of the fractional ratios. For example, if a word problem says a 3 foot tube weighs 28 pounds and then asks how much would a 2 1/4 foot tube weighs, you would keep the length of the tube as the denominator in both fractions. You could write the length as the numerator instead, if you prefer proper fractions, just as long as the length is the numerator in the second fraction too.

References

• Prentice Hall School: Using Proportional Reasoning
• Algebra Help: Solving a Proportion
• Purple Math: Solving Simple Proportions
• Tutor Vista: Solving Proportions with Variables