# Is this a weighted average/percentage problem?

Let's say a Marketing company has a total turnover of 10000 \$There are 3 salesmen A,B,C with the following turnovers A = 2000$
B = 3000 $C = 5000$


Now, If the company wants to increase total turnover by 10 %, Should this be split as 10% for all salesmen OR Can 10% be split across A,B,C differently using weighted averages/percentages?

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Explosion of answers! By the way including \\$in your posts will allow the \$ sign to appear. –  mixedmath Jul 19 '11 at 17:02

You can do whatever you like. If you increase each of A, B, and C by 10%, the total will go up 10%. You can also increase A to 3000 and the total increases by 10%. What is your criterion for the decision?

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It depends on company OR below should be an answer. $$10000=A+B+C=2000+3000+5000$$ $$10000\times(1+0.1)=(A+B+C)\times(1+0.1)=(2000+3000+5000)\times(1+0.1)$$ $$\therefore A=2200, B=3300,C=5500$$

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It the mathematical OR - meaning one, the other, or both. And in this case, it's both. Ultimately, throwing an additional 1000 dollars among A, B, and C will always yield a 10% increase, regardless of how it's distributed.

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Increase of total turnover by 10% $\rightarrow 2000x_a+3000x_b+5000x_c = 11000$. So you have 3 unknowns and 1 equation, so you need more constraints to determine a unique solution.
For e.g. $x_a = x_b = x_c = 1.1$ would work (each person increases their turnover by 10%) and so would $x_a = 0.4, x_b = 1.3, x_c = 1.26$ (required turnover of $A$ reduces to 40%, $B$ increases by 30% and $C$ increases by 26%)!