Hi guys-

I am calculating a weighted average like so-

(10/100) * 5 + (40/100) * 10 + (40/100) * 20 + (10/100) * 0 = 12.5

Notice the zero at the end of the right side of the equation.

Now, what if I want the solution of the equation to be 12? Is there a way to mathematically reset the weights so that 12 is the answer? I was thinking that it might be possible to remove the same amount of weight from each number like so-

((20-x) / 100) * 5 + ((40-x) / 100) * 10 + ((40-x) / 100) * 20 + (3* x / 100) * 0 = 12.

I would then solve for x, allocate the unneeded weight to 0, and have 12 be the answer. Is there a better, more rigorous way to re-weight things? Anything involving proportions?

Thanks