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Math Help - Solving an Algebra Formula

  1. #1
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    Solving an Algebra Formula

    I need to solve this equation. The end goal is to be able to create a worksheet where I can set a goal profitability for a project and have the spreadsheet kick out the suggested price. Here is the equation:

    (Price - Labor - Database - Commission)/Price = % profitability

    Labor is assumed to be a constant.

    Commission has the following equation: Commission = (Price - Labor - Database)*.14

    So basically I need to solve for Price and I can't remember for the life of me how to get rid of the parentheses.

    Simple Version: (P - L - D - ((P - L - D)*.14))/P = X (Solve for P)

    Any help would be incredibly appreciated.
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  2. #2
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    Re: Solving an Algebra Formula

    Quote Originally Posted by noeltroy View Post
    I need to solve this equation. The end goal is to be able to create a worksheet where I can set a goal profitability for a project and have the spreadsheet kick out the suggested price. Here is the equation:

    (Price - Labor - Database - Commission)/Price = % profitability

    Labor is assumed to be a constant.

    Commission has the following equation: Commission = (Price - Labor - Database)*.14

    So basically I need to solve for Price and I can't remember for the life of me how to get rid of the parentheses.

    Simple Version: (P - L - D - ((P - L - D)*.14))/P = X (Solve for P)

    Any help would be incredibly appreciated.
    \displaystyle \begin{align*} \frac{P - L - D - 0.14\left( P - L - D \right) }{P} &= X \\ \frac{(1 - 0.14)\left( P - L  - D \right)}{P} &= X \\ \frac{0.86\left( P - L - D \right)}{P} &= X \\ 0.86\left( P - L - D \right) &= X\,P \\ 0.86\,P - 0.86\,L - 0.86\,D &= X\,P \\ 0.86\,P - X\,P &= 0.86\,L + 0.86\,D \\ \left(0.86 - X\right) P &= 0.86\left(L + D\right) \\ P &= \frac{0.86\left( L + D \right) }{0.86 - X}  \end{align*}
    Thanks from noeltroy
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  3. #3
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    Re: Solving an Algebra Formula

    Brilliant! Thanks so much! There were a couple of moves in there I'd forgotten you could do. Really, really helpful. Thanks!
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  4. #4
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    Re: Solving an Algebra Formula

    Being lazy, I'd set L + D = K and rewrite:

    P - K - .14(P - K) = XP
    P - K - .14P + .14K = XP
    .86P - XP = K - .14K
    P(.86 - X) = K(1 - .14)
    P = .86K / (.86 - X)
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  5. #5
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    Re: Solving an Algebra Formula

    That is really helpful as well. Thanks!
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