Question

If `y` varies inversely as `x` and `y=725` when `x=20`, what is `x` when `y` is 50?

Answer 1

`x=290`

Explanation:

if `y` varies inversely with `x`, then `y=k/x`
therefore `xy=k`

`20(725)=k`
`k=14,500`

when `y=50`, then `50x=14,500`
dividing both sides by `50` you get
`x=290`

Answer 2

`290`

Explanation:

Inverse variation is given by:

`y=k/x^n`

Where `k` is the constant of variation.

First we find `k`.

From example:

`725=k/20=>k=20*725=14500`

When `y=50`

`:.`

`50=14500/x=>x=14500/50=color(blue)(290)`

Answer 3

`x=290`

Explanation:

`"the initial statement is "yprop1/x`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kxx1/x=k/x`

`"to find k use the given condition"`

`y=725" when "x=20`

`y=k/xrArrk=yx=725xx20=14500`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=14500/x)color(white)(2/2)|)))`

`"when "y=50`

`rArrx=14500/y=14500/50=290`