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Piecewise function: check answer

  1. Feb 9, 2014 #1

    939

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    1. The problem statement, all variables and given/known data

    Make a piecewise function. If possible, please check my work.

    - Salesperson has salary of $500.
    - On first 10 000 of sales, earns 10% commission.
    - On next 10 000 of sales, earns 20% commission.
    - Earns 25% commission on any additional sales.

    (note: didn't simplify to show where I got the numbers)

    2. The attempt at a solution

    500 + 0.10(x), x ≤ 10 000

    500 + 0.10(10 000) + 0.20(x - 10 000), 10 000 < x ≤ 20 000

    500 + 0.10(10 000) + 0.20(20 000) + 0.25(x), x > 20 000
     
  2. jcsd
  3. Feb 9, 2014 #2

    Mark44

    Staff: Mentor

    The last line has an error. The saleman earns a 25% commission on "any additional sales." That means any sales over $20,000.
     
  4. Feb 9, 2014 #3

    939

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    Thanks! But doesn't x > 20 000 show that sales must be over 20 000? (i.e. in the function, you would only multiply x by 0.25 if sales, x, were over 20 000)
     
  5. Feb 9, 2014 #4

    haruspex

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    Yes, the sales are over 20,000, but the 25% commission is only on the excess over 20,000.
    You did it correctly in the middle line: ..., 0.20(x - 10 000), ...
     
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