# Interaction of two values

I am a mathematically-challenged guy struggling (or to say better - having no clue at all) about a problem. I have two values (let's call them value ONE and TWO). The first can go from 55 to 190. The second can be anything i want. By making these two values interact i get different results as value one changes (ranging from 6 to 24). What i'd like to do is to have the same result from this interaction, regardless of numeric value of value one.

Unfortunately i cannot act or change the results directly. However, i can change the numeric value of value two. I reckon there should be a formula that, substituted to value two, would give the the desired result (which - in this case - should always be 6) whatever the first value number is.

Please don't bash me, i know i'm terrible :x

VALUE ONE       VALUE TWO      OBTAINED RESULT      DESIRED RESULT
55              0              16                   6
85              0              19                   6
115             0              24                   6
145             0              28                   6
175             0              32                   6
190             0              34                   6

VALUE ONE       VALUE TWO      OBTAINED RESULT      DESIRED RESULT
55              10             6                    6
85              10             9                    6
115             10             14                   6
145             10             18                   6
175             10             22                   6
190             10             24                   6

VALUE ONE       VALUE TWO      OBTAINED RESULT      DESIRED RESULT
55              20             -6                   6
85              20             -1                   6
115             20             4                    6
145             20             8                    6
175             20             12                   6
190             20             14                   6

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It's not really clear what you're asking. As far as I understand it, you have two inputs and one output. You can only control the second input. You have some outputs for some given inputs. Now you're asking: "how do I select input 2 such that I always get the same outcome?" Is that right? – Raskolnikov Jul 15 '13 at 11:42
Yes, this! Sorry, besides not being very math savvy i'm also not a native english speaker :x – arktoga Jul 15 '13 at 11:44
Could there be some errors in the numbers you gave us? Because the relationship between the variables looks pretty linear to me, except for an oddity, namely the value 19 in the first results table. – Raskolnikov Jul 15 '13 at 11:49
Leaving out the odd one, the relationship looks like this $$\text{RES} = 0.1(\text{VAL1} - 55) + 16 - \text{VAL2}$$. – Raskolnikov Jul 15 '13 at 11:53
So to get $6$ as output everytime, just choose $$\text{VAL2}=0.1(\text{VAL1}-55)+10$$ – Raskolnikov Jul 15 '13 at 11:54

I have to warn you that this is not a generally valid procedure. It just worked because the data seemed to exhibit a linear relationship. And in that case, it is not too difficult to find out what that relationship is. First, look at VALUE TWO and the RESULT. You'll notice that in the second group of data, when VALUE TWO = 10, the results are shifted down by 10. When VALUE TWO = 20, the results are shifted down by 20 w.r.t. the original group.

Focussing on the original group, you'll notice that as you rise by 30 points in VALUE ONE, the result rises by 4 which means that

$$\text{RES} = \frac{4}{30}(\text{VAL1} - 55) + 16 - \text{VAL2}$$

for the complete formula. Now, applying your requirement that the end result should always be 6, you can work out that

$$\text{VAL2} = \frac{4}{30}(\text{VAL1} - 55) + 10$$

by simple algebra.

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Thank you again! Peace! – arktoga Jul 16 '13 at 15:05