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Homework Help: Solve for salary given averages of other salaries

  1. Jan 17, 2017 #1
    My wife is working on problems to study for the GMAT, and asks her fellow math nerd (me) to help on some of them. Originally I had an error and wanted to see if any of you could help me find it, but as I was typing I found it myself! Can I still put this up in case someone stumbles on it and it helps them out? The problem is:

    The average weekly salary of 12 workers and 3 managers in a factory was $600. A manager whose salary was $720 was replaced with a new manager, then the average salary of the team fell to $580. What is the salary of the new manager?

    So basically we start with (from the first sentence)
    where tw represents total worker salary and tm represents total manager salary. Now the second sentence says
    so the first equation is now (having multiplied out the 15 from before) -- also label this eqn1
    continuing with info from the second sentence, we get the second equation for the newly decreased average as
    now simplifying gives -- and labeling this eqn2
    subtract the two equations (eqn1-eqn2)
    for the grand finale...
  2. jcsd
  3. Jan 17, 2017 #2


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    Homework Helper

    Nicely done. Since standardized tests often encourage shortcuts, I'll add a supplemental method which cuts through many of the steps.
    In general, if you wanted to affect a change of -$20 in the average of 15 salaries, you have to have a total change of
    15(-$20)=-$300 to the sum.
    This could be done by reducing one salary by $300, or reducing all salaries by $20, or anywhere in between.
    Since the only thing you are changing is the salary starting at $720, you can apply the -$300 to that.
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