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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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marked as duplicate by Raskolnikov, Did, leonbloy, Arturo Magidin, mixedmath Jul 19 '11 at 17:11

This question was marked as an exact duplicate of an existing question.

Whoa - not cool. This is your other question, with a tidbit added at the end. – mixedmath Jul 19 '11 at 17:03
I was not sure if weighted average method can be applied to both subtotals and deltas in subtotals. I have rephrased my question now – Sathish Jul 19 '11 at 17:12
This question has been closed. You should edit and change your other question (the copy of this one) to reflect your question. – mixedmath Jul 19 '11 at 17:13
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). – mixedmath Jul 19 '11 at 17:14

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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Adding 670 to the income increases Total income to 7370 and If expense remains the same, the percentage of total income and total percentage changes to 69.1 % and 30.1 %. Is there a way to solve this so that the Income percentage is 77% and the expense percentage is 23 %? – Sathish Jul 19 '11 at 18:25
@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. – mixedmath Jul 19 '11 at 19:35

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