Question

If $y$ varies jointly as $a$ and $b$ and inversely as the square root of $c$, and $y=12$ when $a=3,b=2,$ and $c=64$, find $y$ when $a=5,b=2,$ and $c=25.$

• A. $32$
• B. $33$
• C. $23$
• D. None of these

Answer 1

The correct option is A $32$

$y\alpha \frac{ab}{\sqrt{c}}$

$y=\frac{kab}{\sqrt{c}}$

$12=\frac{k\times 3\times 2}{\sqrt{64}}$ when $y=12,a=3,b=2,c=64$

$12=\frac{6k}{8}$

$k=16$

Now when $a=5$

$b=2$

$c=25$

$y=\frac{16\times 5\times 2}{\sqrt{25}}=\frac{16\times 2\times 5}{5}$

$y=32$