Solve 3 variables with 2 equations

• Nov 24th 2010, 06:13 AM
abenedet
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.
• Nov 24th 2010, 01:11 PM
bjhopper
Hi abenedet,
Reduce the unknowns to 2 and write two equations. There is an easy solution.

bjh
• Nov 24th 2010, 07:05 PM
abenedet
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!
• Nov 24th 2010, 08:52 PM
Wilmer
Code:

```1652 @      \$2.25 = \$3,717   1 @  \$1,408.00 = \$1,408 ====                ===== 1653                \$5,125```
Hmmm...who bought the one not on sale?
• Nov 25th 2010, 03:28 AM
bjhopper
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
• Nov 25th 2010, 03:43 AM
Wilmer
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.
• Nov 25th 2010, 05:07 AM
bjhopper
Hi Wilmer,
My solution was wrong since it only works ( not exact integers)when the sales are equal.Thanks for the correction.

bjh
• Nov 25th 2010, 03:48 PM
abenedet
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
• Nov 25th 2010, 04:49 PM
Wilmer
Quote:

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...