# Thread: If C=A+A*B what's A in terms of B & C?

1. ## If C=A+A*B what's A in terms of B & C?

I find myself in the odd situation of actually having to use algebra in real life many many years after leaving school!

If C = A + A * B, how do I find A from knowing B and C? If it makes any difference, A,B & C are all greater than zero.

2. Originally Posted by rbbot
I find myself in the odd situation of actually having to use algebra in real life many many years after leaving school!

If C = A + A * B, how do I find A from knowing B and C? If it makes any difference, A,B & C are all greater than zero.
I'll take $\displaystyle A*B$ as A times B.

$\displaystyle A+AB = C$, the left hand side of this equation has common factor A, we can therefore write it as:

$\displaystyle A(1+B) = C$, then dividing both sides by $\displaystyle 1+B$,

$\displaystyle A = \frac{C}{1+B}$

Hope this helps

3. The thing to remember here, is that your equation $\displaystyle a + a \times b = c$ is equivalent to $\displaystyle a \times 1 + a \times b = c$, and then you clearly see the common factor. As you practice more and more, it will become a reflex.

4. Thanks

5. Why can't you just subtract the product of (A*B) from C? Would this be wrong?
I don't think my method would answer his question because it doesn't simply the equation to A in terms of B and C (it is A in terms of A,B, and C) amd I right?

So...
C = A + (AB) -> (-AB)
C - AB = A

6. Originally Posted by Masterthief1324
Why can't you just subtract the product of (A*B) from C? Would this be wrong?
I don't think my method would answer his question because it doesn't simply the equation to A in terms of B and C (it is A in terms of A,B, and C) amd I right?

So...
C = A + (AB) -> (-AB)
C - AB = A
You can do that, but where does it get you? The thing here is that we were asked to "find A given B and C". The word "find" implies that we should solve for A.

7. Originally Posted by Masterthief1324
I don't think my method would answer his question because it doesn't simply the equation to A in terms of B and C (it is A in terms of A,B, and C) amd I right?
correct.