Elementary Algebra

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

Chapter 8 - Coordinate Geometry and Linear Systems - 8.6 - Elimination-by-Addition Method - Problem Set 8.6: 48

Answer

5 large boxes and 20 small boxes

Work Step by Step

We call x the number of large boxes and y the number of small boxes. Thus, we obtain: $ x + y = 25 $ And $ 3x +7.5y = 97.5$ In order to solve this problem, we multiply one or both of the equations by a value that will make one of the variables cancel. We multiply the top equation by -3, and we multiply the bottom equation by 1. Then, we add the two equations to obtain: $4.5y = 22.5 \\ y =5 $ We plug in the given value into the top equation and solve for the other variable: $ x + 5 = 25 \\ x =20$
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