Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.3 Applications of Linear Equations - Exercise Set 6.3: 9

Answer

The numbers are 19 and 45.

Work Step by Step

step 1 Let x represent the smaller number in the problem. step 2 "the other number exceeds x by 26" = $(x+26)$ "Their sum" = $x+ (x+26)$ step 3 "... equals 64" is written as " = 64". The equation is $x+ (x+26) =64$ step 4 Solve, answer the question. $x+ (x+26) =64\quad$. simplify the LHS $2x+26=64\qquad/-26$ $2x=38\qquad/\div 2$ $x=19$ The smaller number is 19. The other number is 19+26=45 step 5 Check the solution in the original wording of the problem. 45 exceeds 19 by 26. (OK) The sum of 19 and 45 is 64. (OK)
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