Finding X when there are two X's

tryingtoexcelatmath

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Mar 5, 2018
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x*(W)*(Q)*(D)*(F)*(C) + x*(W)*(1-Q)*(P)*(D)*(F)*(C) = Output

I am trying to solve for x but am not sure if I did it right.

1. x * (W*Q*D*F*C + W*(1-Q)*P*D*F*C) = Output
2. x = Output / (W*Q*D*F*C + W*(1-Q)*P*D*F*C) <-- I think this is the end result?

Basically X is my starting point and Output is my ending point. So if I have X dollars I will end with Output dollars. Now what I am trying to solve is, if I have output dollars, how much X dollars do I have?

Thanks in advance.
 
x*(W)*(Q)*(D)*(F)*(C) + x*(W)*(1-Q)*(P)*(D)*(F)*(C) = Output

I am trying to solve for x but am not sure if I did it right.

1. x * (W*Q*D*F*C + W*(1-Q)*P*D*F*C) = Output
2. x = Output / (W*Q*D*F*C + W*(1-Q)*P*D*F*C) <-- I think this is the end result?

Basically X is my starting point and Output is my ending point. So if I have X dollars I will end with Output dollars. Now what I am trying to solve is, if I have output dollars, how much X dollars do I have?

Thanks in advance.
What you have is correct. Simplifying a little, think of it as Ax+ Bx= C (A= (W)*(Q)*(D)*(F)*(C), B= (W)*(1-Q)*(P)*(D)*(F)*(C), and c= Output).

We can "factor" x out on the left: x(A+ B)= C, and then divide both sides by A+ B:
x= C/(A+ B).

What you are saying, correctly, is that if you have "Output" dollars, then you have x= Output / (W*Q*D*F*C + W*(1-Q)*P*D*F*C) dollars.
 
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