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# Algebra Ratios and Proportions Study Guide (page 2)

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## Algebraic Expressions in Ratios

The values in a ratio can also be algebraic expressions. We can use ratios and proportions to solve for the value of the variable in these expressions.

#### Example

The ratio of sopranos to altos in a choir is 5:7. If there are 6 more altos than sopranos in the choir, how many sopranos are in the choir?

The number of sopranos is unknown, so we will let x represent that number. There are 6 more altos than sopranos, which means that the number of altosis equal to x + 6. The ratio of sopranos to altos is 5:7, or . We can write the ratio of actual sopranos, x, to actual altos, x + 6, as a ratio, too: . Since these ratios are equal, we can write a proportion and solve for x:

 7x = 5x + 30 2x = 30 x = 15 There are 15 sopranos in the choir.

#### Tip:

There is more than one way to write a ratio that contains algebraic expressions. In the previous example, if we had wanted to find the number of altos in the choir, we could have let x equal the number of altos, and the number of sopranos would have been x – 6, since there are 6 more altos than sopranos. We would have set equal to , and found that x, the number of altos, is equal to 21. As always, let x represent the value that you are looking to find.

Find practice problems and solutions for these concepts at Algebra Ratios and Proportions Practice Questions.

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