Question

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

Answer 1

Answer:

$x=14$

Step-by-step 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 $y=-1$:

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