Using Ratios to Solve Problems

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We can use ratios to solve algebraic problems similarly to how we use fractions.

For example:

The ratio of girls to boys in a class is 4:7.

If the total number of students is 44, how many girls are in the class?

First of all, because we are given the total number of students and asked about the number of girls, we need to find the relationship (ratio) between the number of girls and total number of students.

Since we can safely assume that every student is either a boy or a girl, we can say that this ratio is equal to girls:(girls+boys), which is 4:11.

Letting x be the number of girls, using fractions, we can say that:

x/44 = 4/11

By cross multiplication and simplification, we can solve for x:

x = 44(4)/11

x = 8

=> Number of girls in class: 8

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