Question

If $x$ varies directly as $y$ and when $x$ is $3$, $y$ is $8$, find $y$ when $x=21$.

Answer 1

The general equation for a direct variation is y = kx

Let $x=3$ and $y=8$

$8=k\cdot 3$

$\frac{8}{3}$ = k

Our equation is now y =(8/3)·x

find y when $x=21$

y = $\frac{8}{3}$·21

y = 56

It's also perfectly fine to set up proportions and it's a bit quicker

This would read : 3 is to 8 as 21 is to y

$\frac{3}{8}$ = $\frac{21}{y}$

cross multiply

$3y=168$

$y=56$