Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.5 - Problem Solving and Using Formulas - Exercise Set - Page 66: 9


$x=19$ $y=45$

Work Step by Step

Step 1. Let $x$ and $y$ be the two numbers. $x$ = the first number $y$ = the second number Step 2. Represent other unknown quantities in terms of the other. Hence, the phrase, "One number exceeds another by 26" --> $x+26=y$ The sum of the numbers is 64 --> $x+y=64$ Step 3. Write the equations that model the conditions. $x+26=y$ -->equation 1 $x+y=64$ -->equation 2 Step 4. Solve the equation and answer the question. Substitute equation 1 to equation 2: $x+(x+26)=64$ $x+x+26=64$ $2x+26=64$ Subtract 26 to both sides: $2x+26-26=64-26$ $2x=38$ $x=19$ Substitute to equation 1: $x+26=y$ $19+26=y$ $y=45$ Step 5. Check the proposed solution in the original wording of the problem. Use equation 2: $x+y=64$ $19+45 = 64$ $64=64$ --> TRUE
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