Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - Chapter 3 Review Problem Set: 48

Answer

The width of the rectangular garden is 10 yards. The length of the rectangular garden is 29 yards.

Work Step by Step

Since the length is stated in terms of the width, we can let w represent the width. The length of the garden is 1 yard shorter than three times its width. Three times its width means 3w. 1 yard shorter than three times its width means 3w - 1. So, the length of the garden is 3w - 1. The formula for the perimeter of the rectangle is width + width + length + length The perimeter of the rectangle is 78 yards, so we set up the following equation: w + w + 3w - 1 + 3w - 1 = 78 8w - 2 = 78 8w = 80 Divide both sides by 8. w = 10 The width of the rectangular garden is 10 yards. The length of the rectangular garden is 3 $\times$ 10 - 1 = 29 yards.
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