# How to determine the operation(s) needed to obtain same value for variable in two formulas?

First question on Math.stackexchange so please bear with me as I am not sure of the terminology (or formatting syntax) to be used. I have read the FAQ, List of Common questions and the formatting FAQ (which is still confusing me). I do not see an issue with posting this question here, nor see its premise answered in the common questions. (Please add tags as appropriate, I do not see one for 'This isn't homework, but I would greatly appreciate it if someone would explain to me just WTF is going on!')

The problem A colleague presented a mathematical equation to me in hopes that I could 'solve it' for them. The person explained the results they are expecting, however I am entirely unsure how to come to or provide a solution.

The problem presented is thus:

Given a product(?) and a pseudo formula with static numbers, determine the variable (s). Given two pseudo formulas, s must be the same numbers in both formulas.

Unknown is the operation(s) needed in order come to the right solution. That is, we know the values of all values except for the variable s. How do we come to the determine the variable, while ensuring the variable is the same in the future. s should be static because the other numbers in these formulas will be variables themselves.

Ex values

$$1.27 = \frac{39500 \;(?operations?)\; s}{255}\tag{1}$$

$$1.07 = \frac{39500 \;(?operations?)\; s}{241}\tag{2}$$

The attempted solution I took the problem to mean 'Determine the operation(s) needed to prove that s is the same in both this formulas.'

I started with simple multiplication on the separate formulas: $$1.27 = \frac{(39500 \times s)}{255}$$

$$1.07 = \frac{(39500 \times s )}{241}$$

This attempted solution gives $s = 0.00819873$ and $s = 0.00722325$, but $0.00819873 \neq 0.00722325$; therefore it is not correct. I really am not a particularly smart math guy, and so the limit of my knowledge has been reached after attempting additional operations and not getting anywhere near a solution.

The question(s)

Is this even solvable, without knowing precisely the operations required? How? What methods would I take to designing the formula in order to know the value of s as a constant afterward?? What is the formula? WHAT IS s?!

• That's pretty vague... Oct 31, 2012 at 19:45
• @amwhy I assume the unknown operations in each unit must be identical. Such a formula would be to figure out the sum, based on the formula with S being the constant. But first, S, must be determined based data from previous iterations! Welcome to my daily headache of 'Make me a <project>, I need it in an hour' and 'Why isn't crappy idea working properly'. It (and this question) IS pretty vague! Oct 31, 2012 at 20:52

## 1 Answer

Initially a comment:

Did you consider that the operation(s) used in the first "equation" may not be the operation(s) used in the second "equation"? Unless the "unknown operation(s)" used in each must be identical? If so, then please clarify.

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Answer (given reply to comment above):

Since you want identical operators in each formula, in that case, the numerators, whatever the operation(s) by s, will remain the same, prior to dividing by the respective denominators:

In that case, I'm afraid there is no solution (i.e., no such operation):

Let '$\#$' denote the unknown "operation(s)";

Let $x = 39500 \;\#\; s$ .

Then you can express your problem as that of finding an $x$ that solves both $$\frac{x}{255} = 1.27\quad(x=323.85)\tag{1}$$ $\quad\quad\quad\quad$ AND $$\frac{x}{241} = 1.07\quad(x = 257.87)\tag{2}$$

If you could find such an $x$ (?!), then you'd see more readily how to obtain $\#$ from $x = 39500\, \# \,s$ .

I maintain, though, that since solving for $x$ in each expression above yields a different value for $x$, that unless the operations are different in each formula, say $\#_1$ in the first, distinct from $\#_2$ in the second, such that

$$\frac{39500\;\#_1 \; s}{255} = 1.27\tag{1}$$

$$\frac{39500\;\#_2\; s}{241} = 1.07\tag{2},$$ then there is no solution to your problem.

To get the result you seek, the operations must be such that the numerator of your first equation increases more than the second, or the numerator of the second decreases more than that of the first, etc., i.e., a given s must operate differently in the first equation than in the second equation. Finding the distinct operations required would be an interesting problem.

• Thanks for your reply, and the elaborate explination. I'll chalk this up to a learning experience and at my current level 'unsolvable without more information'. Nov 1, 2012 at 17:28
• I am intrested to this problem too. The binary operation $\#$ must have two values since $39500\#s=\{255\times1.27; 241\times 1.07\}$ maybe that can help us to find a solution? @PenguinCoder Apr 3, 2013 at 9:30