Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.5 Formulas, Applications, and Variation - 7.5 Exercise Set: 23

Answer

$q=\frac{pf}{p-f}$

Work Step by Step

Eliminate the fractions by multiplying the LCD $pqf$ to both sides of the equation: $$\require{cancel} (pqf) \cdot \left(\frac{1}{p} + \frac{1}{q}\right)=(pqf)(\frac{1}{f}) \\(pqf) \cdot \left(\frac{1}{p} + \frac{1}{q}\right)=pq$$ Distribute $pqf$: $$pqf(\frac{1}{p}) + pqf(\frac{1}{q})=pq \\\frac{pqf}{p} + \frac{pqf}{q}=pq \\qf+pf=pq$$ Subtract $(qf)$ from both sides: $$qf+pf-qf=pq-qf \\pf=pq-qf$$ Factor out $q$: $$pf=q(p-f)$$ Divide $p-f$ to both sides of the equation: $$\frac{pf}{p-f}=\frac{q(p-f)}{p-f} \\\frac{pf}{p-f}=q$$
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