Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Cumulative Review Exercises - Page 1128: 38


At $2000$ dollars in sales the earnings will be the same.

Work Step by Step

Let us assume that at $ x $ dollar in sales, the earnings are the same. Now, the equations for the two cases become: 1: $\$200$ and $5\%$ commission on sales, $200+\frac{5x}{100}$ 2: $15\%$ commission on sales, $\frac{15x}{100}$ Then, for them to be the same we equate them: $\begin{align} & 200+\frac{5x}{100}=\frac{15x}{100} \\ & \frac{15x}{100}-\frac{5x}{100}=200 \\ & \frac{15x-5x}{100}=200 \\ & \frac{10x}{100}=200 \end{align}$ And simplify it further: $\begin{align} & x=200\cdot \left( \frac{100}{10} \right) \\ & x=2000 \end{align}$ Thus, the dollars of sales for which the earnings will be the same is $\$2000$.
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