Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Test - Page 331: 20

Answer

The lab assistant should add 120cc of the 12% saline solution.

Work Step by Step

Let $x$ be the amount (in cc) of the 12% solution and $y$ be the amount of the 16% solution. Equation 1: $x+80=y$ Equation 2: $0.12x+0.22(80)=0.16y$ Substitute equation 1 to equation 2: $$0.12x+0.22(80)=0.16y$$ $$0.12x+0.22(80)=0.16(x+80)$$ $$0.12x+17.6=0.16x+12.8$$ Subtract $17.6$ from both sides: $$0.12x+17.6-17.6=0.16x+12.8-17.6$$ $$0.12x=0.16x-4.8$$ Subtract $0.16x$ from both sides: $$0.12x-0.16x=0.16x-0.16x-4.8$$ $$-0.04x=-4.8$$ Divide both sides by $-0.04$: $$\frac{-0.04x}{-0.04}=\frac{-4.8}{-0.04}$$ $$x=120$$ Substitute this value of $x$ to equation 1: $$x+80=y$$ $$120+80=y$$ $$y=200$$ Check using equation 2: $$0.12x+0.22(80)=0.16y$$ $$0.12(120)+0.22(80)=0.16(200)$$ $$14.4+17.6=32$$ $$32=32$$
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