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

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Answer 1 · 2016-06-06T14:39:11

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

Method 1:
In an inverse variation as one variable increases the other decreases.
$y \propto \frac{1}{x}$ $color(blue)(yprop1/x$

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

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

$y = \frac{k}{x}$ $color(blue)(y = k /x$

We now substitute the value of variables as provided:

$x = 10, y = 50$ $x=10 , y =50$

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

$k = 50 \cdot 10 = 500$ $k = 50 * 10 = color(green)(500$

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

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

$y = 25$ $color(purple)(y = 25$

Method 2:

As per data provided when $x = 10$ $color(green)(x =10)$ , $y = 50$ $y =50$

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

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

So, $y = \frac{50}{2}, y = 25$ $y = 50/2, color(purple)(y = 25$