# Y varies inversely as x, and y = 50 when x = 10. What is the value of y when x = 20?

Jun 6, 2016

When $x = 20$ the value of color(purple)(y = 25

#### Explanation:

Method 1:
In an inverse variation as one variable increases the other decreases.
color(blue)(yprop1/x

We now insert a constant $k$ into the equation:

$y = k \cdot \frac{1}{x}$

color(blue)(y = k /x

We now substitute the value of variables as provided:

$x = 10 , y = 50$

$50 = \frac{k}{10}$

k = 50 * 10 = color(green)(500

Now we use the value of this constant to find $y :$
As per data provided $x = 20$
color(blue)(y = k /x

$y = \frac{500}{20}$

color(purple)(y = 25

Method 2:

As per data provided when $\textcolor{g r e e n}{x = 10}$ , $y = 50$

So, when $x = 20$, the value is doubled from the initial value of $x$,
(20 = color(green)(10) * 2)

Since the value of $x$ is doubled , the value of $y$ will have to be halved from the initial value, since there is an inverse variation.

So, y = 50/2, color(purple)(y = 25