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: 68

Answer

One of them will receive 500 dollars, and the other one will receive 750 dollars.

Work Step by Step

Let X represent the amount one of them will receive. Since both of them will receive 1250 dollars in total, the other one will receive 1250 - X. This sum is to be divided in the ratio of 2 to 3, or $\frac{2}{3}$. Now, let’s set up a proportion with the ratio given and a ratio which compares the amounts of money received. So, $\frac{2}{3}$ = $\frac{X}{1250 - X}$. To solve this equation, we equate the cross products. 2 $\times$ (1250 - X) = 3 $\times$ X 2500 - 2X = 3X 2500 = 5X Divide both sides by 5. X = 500 One of them will receive 500 dollars, and the other one will receive 1250 - 500 = 750 dollars.
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