Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1: 66

Answer

There are 3875 male students at the university. There are 3100 female students at the university.

Work Step by Step

Let X represent the number of male students. Because there are 6975 students at the university, the number of female students is 6975 - X. The ratio of male students to female students is 5 to 4, or $\frac{5}{4}$. Now, let’s set up a proportion with the ratio given and a ratio which compares the number of male students to the number of female students. So, $\frac{5}{4}$ = $\frac{X}{6975 - X}$ To solve this equation, we equate the cross products. 5 $\times$ (6975 - X) = 4 $\times$ X 34875 - 5X = 4X 34875 = 9X Divide both sides by 9. X = 3875 There are 3875 male students at the university. There are 6975 - 3875 = 3100 female students at the university.
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