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 - Page 486: 29



Work Step by Step

Use the rule $\frac{a}{b}=\frac{c}{d}\longrightarrow ad=bc$ to obtain: $$S(1-r)=a \\S(1)-S(r)=a \\S-rS=a$$ Subtract $S$ from both sides of the equation: $$S-rS-S=a-S \\-rS=a-S$$ Divide $-S$ to both sides of the equation: $$\frac{-rS}{-S}=\frac{a-S}{-S} \\r=\frac{a-S}{-S} \\r=\frac{a}{-S} -\frac{S}{-S} \\r=-\frac{a}{S}-(-1) \\r=-\frac{a}{S} + 1 \\\color{blue}{r=1-\frac{a}{S}}$$
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