Reduce the unknowns to 2 and write two equations. There is an easy solution.
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.
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...