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.
-----------
1.
$y$ varies directly as $a:\qquad y=ka$
$y$ varies directly as $b:\qquad y=kb$
$y$ varies inversely as $ \displaystyle \sqrt{c}:\qquad y=\frac{k}{\sqrt{c}},$
Combined (jointly): $\displaystyle \qquad y=\frac{kab}{\sqrt{c}}.$
2.
$12=\displaystyle \frac{k(3)(2)}{\sqrt{25}}$
$12=\displaystyle \frac{6k}{5}\qquad/\times\frac{5}{6}$
$k=\displaystyle \frac{12\cdot 5}{6}=10$
3.
$ y=\displaystyle \frac{10ab}{\sqrt{c}}$
4.
$ y=\displaystyle \frac{10(5)(3)}{\sqrt{9}}=\frac{10(5)(3)}{3}=50$
