Elementary Algebra

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

Appendix - Extra Word Problems - Page 523: 16



Work Step by Step

Let the unknown number be $x$. Three-eight of this number is $\frac{3}{8}x$ while five-sixth of this number is $\frac{5}{6}x$. Since when three-eighths of a number is subtracted from five-sixths of the number, the result is 22, we write the following equation and solve: $\frac{5}{6}x-\frac{3}{8}x=22$ $\frac{5x}{6}-\frac{3x}{8}=22$ $\frac{5x(4)-3(3x)}{24}=22$ $\frac{20x-9x}{24}=22$ $\frac{11x}{24}=22$ $11x=528$ $x=\frac{528}{11}=48$ Therefore, the unknown number is 48.
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