# If y Varies Inversely As x and if y = 8 When x = 2.5, how do you find x when y = 2?

Nov 6, 2017

$x = 10$ when $y = 2$

#### Explanation:

If $y$ varies inversely as $x$

Then $y = \frac{k}{x}$ for some constant $k$

Since $y = 8$ when $x = 2.5$

$8 = \frac{k}{2.5}$

$\therefore k = 8 \times 2.5 = 20$

We are asked to find $x$ when $y = 2$

Hence, $2 = \frac{20}{x} \to x = \frac{20}{2}$

$x = 10$