Question

Variable A varies directly with P and Q. If A=42 when P=8 and Q=9, how do you find A when P=44 and Q=7?

Answer 1

`A=539/3=179 2/3`

Explanation:

As `A` varies directly with `P` and `Q`, we have

`ApropP` and `ApropQ` i.e. `ApropPxxQ`

Hence `A=kxxPxxQ`, where `k` is a constant.

Now if `A=42`, when `P=8` and `Q=9`, we have

`42=kxx8xx9` or `k=42/(8xx9)=(cancel2xxcancel3xx7)/(cancel2xx4xx3xxcancel3)=7/12`

Hence, when `P=44` and `Q=7`,

`A=7/12xx44xx7=7/(cancel4xx3)xxcancel4xx11xx7=539/3=179 2/3`