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.

Re: Solving an Algebra Formula

Quote:

Originally Posted by

**noeltroy** 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.

$\displaystyle \displaystyle \begin{align*} \frac{P - L - D - 0.14\left( P - L - D \right) }{P} &= X \\ \frac{(1 - 0.14)\left( P - L - D \right)}{P} &= X \\ \frac{0.86\left( P - L - D \right)}{P} &= X \\ 0.86\left( P - L - D \right) &= X\,P \\ 0.86\,P - 0.86\,L - 0.86\,D &= X\,P \\ 0.86\,P - X\,P &= 0.86\,L + 0.86\,D \\ \left(0.86 - X\right) P &= 0.86\left(L + D\right) \\ P &= \frac{0.86\left( L + D \right) }{0.86 - X} \end{align*}$

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!

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)

Re: Solving an Algebra Formula

That is really helpful as well. Thanks!