Question

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

Answer 1

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 * 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`