Question

If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?

Answer 1

`x=14`

Explanation:

If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.

Therefore, if
`(x-4)` and
`(y+3)` vary inversely, their product will be the same for all values of
`x-4` and
`y+3`.

Let
`x=8` and
`y=2` as given in the problem. Substitute values:

`(8-4)(2+3)=(4)(5)=20`

Hence, the maintained product is
`20`.

Thus, we have the following equation:

`(x-4)(y+3)=20`

Substitute
`y=-1` to find the value of
`x` when
`y=-1`:

`(x-4)(-1+3)=20,\\(x-4)(2)=20,\\x-4=10,\\x=10+4=\boxed{14}`