Elementary Algebra

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

Appendix - Extra Word Problems - Page 524: 31



Work Step by Step

Let the smaller number be $x$ and the larger number be $y$. Since the difference of the two numbers is 27, we obtain: $y-x=27$ When three times the smaller number is subtracted from the larger number, the result is -1, so we write $y-3x=-1$ $y=3x-1$ Therefore, we now have a pair of equations to solve. Substituting the second equation into the first equation, we obtain: $y-x=27$ $3x-1-x=27$ $2x-1=27$ $2x=27+1$ $2x=28$ $x=14$ Substituting the value of $x$ in the first equation to find the value of $y$, we obtain: $y-x=27$ $y-14=27$ $y=27+14$ $y=41$ Therefore, the smaller number is 14 while the larger number is 41.
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