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: 37

Answer

The number we need to find is 18.

Work Step by Step

Let X represent the number we need to find. Two-thirds of the number means $\frac{2}{3}$X. 2 less than two-thirds of the number means $\frac{2}{3}$X - 2. One-half of the number means $\frac{1}{2}$X 1 more than one-half of the number means 1 + $\frac{1}{2}$X. Since both of these expressions are equal, we solve the following equation: $\frac{2}{3}$X - 2 = 1 + $\frac{1}{2}$X $\frac{2}{3}$X - $\frac{1}{2}$X = 3 $\frac{2}{3}$X $\times$ $\frac{2}{2}$ - $\frac{1}{2}$X $\times$ $\frac{3}{3}$= 3 $\frac{4X}{6}$ - $\frac{3X}{6}$ = 3 $\frac{X}{6}$ = 3 Multiply both sides by 6: X = 18
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