# How to calculate the weight individual fractions to equal the weighting of the product of the same fractions

What is the formula to apply a weighting to 2 fractions individually to get the same answer if you weight their product? In the example below 50% * 100% = 50%. Multiplied times 80% (weighting) the answer is 40%. What formula can be used to multiply 50% and 100% individually to also arrive at 40% when you multiply the result. Example: (50% * A) = X and (100% * B) = Y; and X * Y = 40%. I am looking for the formula to arrive at A and B.

Value 1 50.0% Value 2 100.0% Product of 1 and 2 50.0% Weighting 80% Weighting * Product 40%

Weighting
A? X = Value 1 * Weighting A
B? Y = Value 2 * Weighting B
X * Y = 40%

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The question's phrasing is a bit difficult to follow, could you try to re-phrase the question? The last line is specially confusing. – NoChance Oct 8 '12 at 22:29

There is more than one answer.

So for example if A=80% and B=100% then you have (50% * 80%) * (100% * 100%) = 40%

Or if A=100% and B=80% then you have (50% * 100%) * (100% * 80%) = 40%

Or if A=B=89.4427191% then you have (50% * 89.4427191%) * (100% * 89.4427191%) = 40% or very close to it, noting that $\sqrt{0.8} \approx 0.894427191$.

The only important thing is that A*B=80%, since multiplication is commutative.

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Thanks! I was looking for the number where A=B, but did not specify. I appreciate the help. – user44051 Oct 9 '12 at 1:37