Answer
$\displaystyle \frac{5}{6}$
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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1.
$y$ varies directly as $x$ or $y$ is directly proportional to $x$.
$y=kx$
$y$ varies inversely as $z^{2}$ or $y$ is inversely proportional to $z^{2}$.
$y=\displaystyle \frac{k}{z^{2}}$
Combined: $y=\displaystyle \frac{kx}{z^{2}}$
2.
$20=\displaystyle \frac{k(50)}{5^{2}} $
$20=2k \qquad /\div 2$
$k=10$
3.
$y=\displaystyle \frac{10x}{z^{2}}$
4.
$y=\displaystyle \frac{10(3)}{6^{2}}=\frac{30}{36}=\frac{5}{6}$