Solving for two variables

[Bay]

The only current input is the Discount Offer at C7. The rest of the values are calculated.
I would like to add a cell where the only input would be at C14 and the rest of the values would be calculated.
I have used the "Goal Seek" function and the "Solver" at C13, but I would like to have it part of the sheet.
I have spent several hours on this, but the two variables have me stumped :-(

[MrShorty]

It looks like it is just one variable to solve for, unless I am misunderstanding the problem. As I understand it, you want to be able to enter a value in C14 (that should be the same as C13), then calculate the values in C11, C9, C8, and C7 (the other cells appear to be constant values). As I indicated in the other thread, it seems like it should be simple (if tedious) algebra:

Currently:
C13=C3-C11
C11=C8+C9+C10
C9=0.07*C8
C8=C6-C7
Given the values in C3, C6, and C7 we can calculate all of the others.

Goal -- using the same formulas, but have C3, C6, and C13 as givens and calculate the others.
Solve for C11 from the formula for C13: C13=C3-C11 -> C11=C3-C13. Enter this formula into C11.
Solve for C7 from the formula for C11 (this one is a little trickier):
C11=C8+C9+C10 -> substitute for C8 and C9
C11=C6-C7+0.07*C8+C10 -> still need to get rid of the C8 so substitute
C11=(C6-C7)+0.07*(C6-C7)+C10 -> Combine like terms and get rid of parentheses
C11=1.07*C6-1.07*C7+C10 -> Finish solving for C7 (Can I assume you can solve for C7 from here?)

Once you have solved for C7, put that formula into C7, C8 and C9 are then the same as they are currently.

That should do it (assuming you can finish the algebra solution). Questions?

[Bay]

MrShorty

I assumed the two variables were the input and the tax calculation. I guess the calculation requires only the tax to be calculated, hence the one variable.
I uploaded a slightly easier to see sheet showing the old Example 1 and the desired Example 2
I added the same value in to E13, but that can be of any value.
I see what you did so far, but alas I could not derive the formula for E7. I need to take a refresher! Last time I played with equations was 1965.
Tnx for your continued help

[Bay]

MrShorty
I did put the correct formula E3 -E13 in E11 after I sent reply above. Sorry for any confusion.

[MrShorty]

Continuing from above:
C11=1.07*C6-1.07*C7+C10 -> Finish solving for C7 (Can I assume you can solve for C7 from here?) subtract 1.07*C6+C10 from each side->
C11-1.07*C6-C10=-1.07*C7 -> Divide both sides by -1.07
C7=(C11-1.07*C6-C10)/-1.07 -- enter this formula into C7 (or E7 in the new sheet substituting E for C).

Also, remember to replace C11 (E11) with =C3-C13 or =E3-E13

[Bay]

Thanks a million for your answer.
I managed after a nice glass of wine:
E11=1.07*E6-1.07*E7+E10
E11+1.07*E7=1.07*E6+E10
1.07*E7=1.07*E6+E10-E11
E7=(1.07*E6+E10-E11)/1.07

Plunked it in to E7 and voila! it works.