Elementary Algebra

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

Appendix - Extra Word Problems: 30

Answer

36,42

Work Step by Step

Let the smaller number be $x$ and the larger number be $y$. Since the sum of the two numbers is 78, we obtain: $x+y=78$ Since the smaller number subtracted from the larger number produces 6, we know: $y-x=6$ $y=6+x$ Therefore, we now have a pair of equations. Substituting the second equation into the first equation, we obtain: $x+y=78$ $x+(6+x)=78$ $2x+6=78$ $2x=78-6$ $2x=72$ $x=36$ Substituting the value of $x$ in the first equation to find the value of $y$, we obtain: $x+y=78$ $36+y=78$ $y=78-36$ $y=42$ Therefore, the smaller number is 36 while the larger number is 42.
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