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

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:

$y = k * 1/x$

$color(blue)(y = k /x$

We now substitute the value of variables as provided:

$x=10 , y =50$

$50 = k /10$

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

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

$y = 500 /20$

$color(purple)(y = 25$

Method 2:

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

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