Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Section 4.3 - Systems of Linear Equations and Problem Solving - Exercise Set - Page 230: 7

Answer

$20$ quarts of $4\%$ butterfat milk and $40$ quarts of $1\%$ butterfat milk

Work Step by Step

Let $x$ represent the number of $4\%$ butterfat milk quarts and let $y$ represent the number of $1\%$ butterfat milk quarts. To simplify, use whole numbers as the coefficients for the percentages as opposed to decimals. Multiply $60$ and $2$ to obtain the expected total percentage of butterfat milk. $4x + y = 60 \times 2$ $4x + y = 120$ Equation $(1)$ $y = 120-4x$ There are $60$ total quarts. $x+y = 60$ Equation $(2)$ Substitute $y$ into Equation $(2)$ $x+(120-4x)=60$ $-3x=-60$ $x=20$ Solve for $y$ by substituting $x$. $y=120-4(20)$ $y=40$ $20$ quarts of $4\%$ butterfat milk and $40$ quarts of $1\%$ butterfat milk
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