Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.2 Applications and Modeling with Linear Equations - 1.2 Exercises - Page 103: 33

Answer

$4$ mL

Work Step by Step

If the saline has $ 4\%$ concentration, it means that $ 96\%$ is water, $4\% $salt... Set up a table: $\left[\begin{array}{ccc} \% \text{water} & \text{mL of } & \text{mL of water}\\ & \text{ the solution} & \\ 100\% & x & x\\ 94\% & 8 & 7.52\\ & & \\ 96\% & (x+8) & 0.96(x+8) \end{array}\right]$ The equation to solve is: $ x+7.52=0.96(x+8)\qquad$ ... multiply with $100$ $100x+752=96(x+8)$ $ 100x+752=96x+768 \qquad$ ... add $(-96x-752)$ $4x=16$ $x=4$ mL
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