Question

If $y$ varies directly as $x$ and inversely as $z,$ and $y=22$ when $x=4$ and $z=6$, find $y$ when $x=10$ and $z=25.$

• A. $\frac{66}{5}$
• B. $\frac{65}{4}$
• C. $\frac{63}{2}$
• D. None of these

Answer 1

Answer: (A)

$\frac{66}{5}$

$y\alpha \frac{x}{z}$

$y=\frac{kx}{z}$

when $y=22$

$x=4$

$z=6$

$22=\frac{4k}{6}$

$k=33$

when $x=10$

$z=25$

$y=?$

$y=33\times \frac{10}{25}=\frac{66}{5}$