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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:

The turnovers have two components - Income and Expenses:

A = 2000  B = 3000 $ C = 5000 $ Ia = 80% = 1600 $      Ib = 70% = 2100 $  Ic = 60% = 3000 $ Ea = 20% = 400 $ Eb = 30% = 900 $ Ec = 40% = 2000 $ Total Income = 6700 USD = 67% Total Expense = 3300 USD = 33% 

Now, If the company wants to increase total Income by 10 %, How should this increase be split across the Incomes of A,B,C? Is this a weighted average/percentage increase problem?

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    Also note that you can pick up a copy of the whole post and move it over, if absolutely necessary. Or the post history by clicking on the time (e.g. edited **3 mins ago**).2011-07-19

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Firstly, this is a duplicate of your other question. Secondly, it has the same answer: if you want to increase the income, which is at 6700, by 10%, then adding 670 income to the three in any particular way will do it. If you wanted to maintain the income/expense ratio for each person, then it is slightly less trivial.

In this case, you want $0.8 A_+ + 0.7 B_+ + 0.6 C_+ = 670$. Here, I use letter$_+$ to indicate the additional turnover to the person with that letter. In a sense, that's a weighted average problem... but that's not how I would solve it (I would do it as above).

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    @Sathish: yes - but that is not increasing the income by 10%. Now you have a weighted average. You are solving $\dfrac{6700 + D}{10000 + D} = 0.77$. This has a solution - but I'll let you find it.2011-07-19