How do I solve a equation with two knowns and two unknowns?

Question

How do I solve a equation with two knowns and two unknowns?

Given: Four variables A, B, C and D related by the equation A = (B x C) / (B + D).

Step 1: A and D are known values, derive a equation to determine the relationship between known variables A, D and unknown variables B, C for the next step.

Step 2: Using the equation derived in Step 1 for a different value of A calculate D.

Show both equations and steps taken.

Does this problem have a name or is it used for a pratical purpose?

Answer 1

The goal of this question is to use algebraic methods to solve the equation A = (B x C) / (B + D) for an expression involving A and D only.

     A = (B x C) / (B + D)                                  multiply both sides by (B + D)

     A (B + D) = (B x C)                                    distribute A over (B + D)

     (A x B) + (A x D) = (B x C)                         subtract the term (A x B) from both sides

      A x D = (B x C) - (B x A)       {AxB = BxA :: commutativity}  distribute B out of (B x C) and (B x A)

      A x D = B (C - A)                 at this point you should be able to find two factors of the product of A x D and call one of them B and the other when added to A will give you C.

If you then keep B and C the same, and change A to the new value, you should be able to determine the required value of D.

I cannot think of a particular name or purpose for this problem.