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I would like to understand, proportionally, how much of someone's new salary is attributed to an increase in both their number of hours worked, and increased dolar wage respectively. Both these variables changed simultaneously, now I'd like to know how much each affects their new salary.

For example:

An employee's old wage was 20 hrs x \$10 = \$200.

Their new wage is 25 hrs x \$15 = \$375.

I want to know how many \$ of their new wage can be attributed to the increase in hours and how much is due to increase in wage.

I'm finding it's not as simple as knowing that hours increased 25% and rate increased 50%, since that increased rate compounds total hours worked. Any direction to point me down is much appreciated.

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up vote 1 down vote accepted

He is being paid \$100 more for the 20 hours he was already working (at a 50% salary increase), and \$75 for the extra five hours (at the new rate).

You could say that \$100 out of the \$175 total increase are entirely due to the increase in salary (that would be 4/7ths, or about 57.14% of the increase), and \$75 out of \$175 are entirely due to the new hours (3/7ths, or about 42.86% of the increase).

I'm not sure that would be entirely clear to someone listening to you saying that, though.

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Alternately, you could say that he worked the 5 new hours at \$10/hr for \$50, then got the raise on all the new hours \$5/hr x 25 hrs =\$125. I'm not sure there is a well-defined answer as it depends on the order you apply things. – Ross Millikan Sep 24 '11 at 22:14
@Ross: I agree; what I did was the best I could figure out if we really want to completely separate the money obtained from the extra hours, and the money obtained from the raise. The raise would only apply to the "old hours", while the new salary applies de nuovo to the extra hours. But there's no way anyone would understand what I mean without an explanation if I just said that, hence my final paragraph... – Arturo Magidin Sep 24 '11 at 22:37

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