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Math Help - Solve 3 variables with 2 equations

  1. #1
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    Solve 3 variables with 2 equations

    Here is the problem:

    Total sales are $5125 and units sold are 1653. Units can be sold either on sale or not on sale. The price on sale or feature sale price (FSP) was $2.25. How many units were sold on sale?

    I can derive 2 formulas, but I have 3 variables to solve. Here's how far I have gotten:

    Regular price = RSP
    Units sold on Sale = Promoted volume (PV)
    Units sold at regular = non-promoted volume (NPV)
    Total volume = TV

    Equation 1: TV = PV + NPV
    Equation 2: Total Sales = (RSP x NPV) + (FSP x PV) or $5125 = (RSP x NPV) + 2.25PV

    Given these two equations (or any other equations that you can think of), how can I solve for PV?

    Any help will be greatly appreciated.
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  2. #2
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    Hi abenedet,
    Reduce the unknowns to 2 and write two equations. There is an easy solution.


    bjh
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  3. #3
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    That's where I am stuck. How do I reduce it to two unknowns? If I can get it to that point, I think I can take it from there.

    Thanks!
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  4. #4
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    Code:
    1652 @      $2.25 = $3,717
       1 @  $1,408.00 = $1,408
    ====                 =====
    1653                $5,125
    Hmmm...who bought the one not on sale?
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  5. #5
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    Hi abenedet,
    Let x= units sold at sale price $ 2.25
    1653-x = units sold at regular price
    Let y= regular price
    Equation 1 equates sales by units to $5125
    Equation 2 defines y


    bjh
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  6. #6
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    Ya; per BJ: 2.25x + y(1653 - x) = 5125
    But you can have a solution for any value of x < 1653.
    Example: x = 1000
    2.25(1000) + y(1653 - 1000) = 5125
    y = 4.4027565...

    Only solution that has "integer results" is x=1652 and y=1408.
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  7. #7
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    Hi Wilmer,
    My solution was wrong since it only works ( not exact integers)when the sales are equal.Thanks for the correction.


    bjh
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  8. #8
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    Thanks everyone for the responses.

    Is there another way to solve this without fixing x to be an exact #? That is, is there any other formula that can be derived to find the exact solution?

    Thanks again
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  9. #9
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    Quote Originally Posted by abenedet View Post
    Is there another way to solve this without fixing x to be an exact #? That is, is there any other formula that can be derived to find the exact solution?
    NO.
    We have 1 equation: 2.25x + y(1653 - x) = 5125;
    equation has 2 variables: x and y.
    With 2 variables, you need 2 equations for an exact solution.
    Like, to illustrate with something simple:
    a + b = 5
    1 + 4 = 5
    2 + 3 = 5
    3 + 2 = 5
    4 + 1 = 5
    5 + 0 = 5
    6 - 1 = 5
    and so on...
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