Question

y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necessary.

Answer 1

3.7

Explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant. We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

`y=(k)/(x)`

So they actually give us k=8.88 and y=2.4 so let's input this:

`2.4=(8.88)/(x)`

We need to solve this equation for x. You can do your favorite thing in cross-multiply. But how, Freckles? Well just slap a 1 underneath that 2.4. You can do that because 2.4/1 is still 2.4.

`(2.4)/(1)=(8.88)/(x)`

Cross-multiply:

`2.4x=8.88(1)`

`2.4x=8.88`

Divide both sides by 2.4:

`x=(8.88)/(2.4)`

`x=3.7` when
`y=2.4`.