# Suppose x varies inversely with y. If X = 10 when y = 5 how do you find x when y = 14?

Jun 28, 2016

Construct a variation equation and solve for $x$ to get $x = \frac{25}{7}$.

#### Explanation:

When we say "$x$ varies inversely with $y$", we mean that when $x$ increases, $y$ decreases, and vice versa. Mathematically, this is expressed as:
$y = \frac{k}{x}$
Where $k$ is referred to as the constant of variation.

We are told $x = 10$ when $y = 5$, so:
$5 = \frac{k}{10}$
$\to 10 \cdot 5 = k \to 50 = k$

Our equation is:
$y = \frac{50}{x}$

If $y = 14$, then
$14 = \frac{50}{x}$
$\to x = \frac{50}{14} = \frac{25}{7}$