# If x varies inversely as y and directly as t, and x = 12 when t = 10 and y = 25, how do you find y when x is 6 and t = 3?

Aug 11, 2017

$y = 15$

#### Explanation:

$\text{the initial statement is } x \propto \frac{t}{y}$

$\text{to convert to an equation multiply by k the constant of}$
$\text{variation}$

$\Rightarrow x = \frac{k t}{y}$

$\text{to find k use the given condition}$

$x = 12 \text{ when "t=10" and } y = 25$

$x = \frac{k t}{y} \Rightarrow k = \frac{x y}{t} = \frac{12 \times 25}{10} = 30$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{x = \frac{30 t}{y}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "x=6" and } t = 3$

$y = \frac{30 t}{x} = \frac{30 \times 3}{6} = 15$