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?

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Answer 1 · 2016-08-05T06:39:21

$A = \frac{539}{3} = 179 \frac{2}{3}$ $A=539/3=179 2/3$

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

$A \propto P$ $ApropP$ and $A \propto Q$ $ApropQ$ i.e. $A \propto P \times Q$ $ApropPxxQ$

Hence $A = k \times P \times Q$ $A=kxxPxxQ$ , where $k$ $k$ is a constant.

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

$42 = k \times 8 \times 9$ $42=kxx8xx9$ or $k=42/(8xx9)=(cancel2xxcancel3xx7)/(cancel2xx4xx3xxcancel3)=7/12$

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

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