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: 64

Answer

The length of the first piece of board is 8 feet. The length of the second piece of board is 20 feet.

Work Step by Step

Let X represent the length of one piece. Since the total length of the board was 28, the length of the other piece is 28 - X. Those lengths are in the ratio of 2 to 5, or $\frac{2}{5}$. So, let's set up a proportion with the ratio given and a ratio which compares the corresponding lengths. So, $\frac{2}{5}$ = $\frac{X}{28 - X}$ To solve this equation, we equate the cross products. 2 $\times$ (28 - X) = 5 $\times$ X 56 - 2X = 5X 56 = 7X Divide both sides by 7 X = 8 The length of the first piece of board is 8 feet. The length of the second piece of board is 28 - 8 = 20 feet.
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