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: 52

Answer

It costs 8 dollars per pound of coffee and 2.75 dollars per pound of butter.

Work Step by Step

We call x the cost per pound of coffee and y the cost per pound of butter. Thus, we obtain: $ 2x + y = 18.75 $ And $ 3x + 2y = 29.5$ 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 -2, and we multiply the bottom equation by 1. Then, we add the two equations to obtain: $-x = -8 \\ x= 8 $ We plug in the given value into the top equation and solve for the other variable: $ 2(8) + y = 18.75 \\ y = 2.75$
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