# Thread: Solve 3 variables with 2 equations

1. ## 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. 2. Hi abenedet, Reduce the unknowns to 2 and write two equations. There is an easy solution. bjh 3. 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! 4. Code: 1652 @$2.25 = $3,717 1 @$1,408.00 = $1,408 ==== ===== 1653$5,125
Hmmm...who bought the one not on sale?

5. 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

6. 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.

7. Hi Wilmer,
My solution was wrong since it only works ( not exact integers)when the sales are equal.Thanks for the correction.

bjh

8. 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

9. Originally Posted by abenedet
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...