Elementary Algebra

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

Appendix - Extra Word Problems - Page 523: 17



Work Step by Step

Let the unknown number be $x$. One-eighth of this number is $\frac{1}{8}x$, one-sixth of this number is $\frac{1}{6}x$, and three-fourth of this number is $\frac{3}{4}x$. Since we know that the sum of 1/8 and 1/6 of this number is subtracted from 3/4 of this number to get 33, we obtain: $\frac{3}{4}x-(\frac{1}{8}x+\frac{1}{6}x)=33$ $\frac{3}{4}x-(\frac{3x+4x}{24})=33$ $\frac{3}{4}x-(\frac{7x}{24})=33$ $\frac{3x(6)-7x}{24}=33$ $\frac{18x-7x}{24}=33$ $11x=792$ $x=\frac{792}{11}=72$ Therefore, the unknown number is 72.
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