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: 45

Answer

5 gallons of 10% and 15 gallons of 20%.

Work Step by Step

We call x the gallons of 10% solution and y the gallons of 20% solution. Thus, we obtain: $ x + y = 20 $ And $ 1.75 = (.1x + .2y )/2 \\ 3.5 = .1x + .2y$ 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 1, and we multiply the bottom equation by -10. Then, we add the two equations to obtain: $ -15 = -y \\ y =15 $ We plug in the given value into the top equation and solve for the other variable: $ x +(15) = 20 \\ x =5$
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