College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.7 - Page 431: 32

Answer

50

Work Step by Step

Solving Variation Problems (see p. 424) 1. $\ \ $Write an equation that models the given English statement. 2. $\ \ $Substitute the given pair of values into the equation in step 1 and find the value of k, the constant of variation. 3. $\ \ $Substitute the value of k into the equation in step 1. 4. $\ \ $Use the equation from step 3 to answer the problem's question. ----------- Let $I_{q}$ be the intelligence quotient, m the mental age, and c the chronological age of a person $I_{q}$ varies directly as $m$, and inversely as $c,\ \displaystyle \qquad I_{q}=\frac{km}{c}$ 2. $125=\displaystyle \frac{k\cdot 25}{20}\qquad /\times\frac{20}{25}$ $\displaystyle \frac{125\cdot 20}{25}=k$ $k=\displaystyle \frac{125\cdot 4}{5}=25\cdot 4=100$ 3. $I_{q}=\displaystyle \frac{100m}{c}$ 4. $m=40, I_{q}=80, c=?$ $80=\displaystyle \frac{100\cdot 40}{c}\qquad/\times\frac{c}{80}$ $c=\displaystyle \frac{100\cdot 40}{80}=\frac{100}{2}=50$ (the chronological age)
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