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.
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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)