SOLUTION: My problem is to find a: {{{(c/x)+(m/a)=c}}} I've already distributed the problem to (ac+mx=acx) but I'm not sure where to go from here. Thank you for the help

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: My problem is to find a: {{{(c/x)+(m/a)=c}}} I've already distributed the problem to (ac+mx=acx) but I'm not sure where to go from here. Thank you for the help      Log On


   

Question 708022: My problem is to find a: %28c%2Fx%29%2B%28m%2Fa%29=c
I've already distributed the problem to (ac+mx=acx) but I'm not sure where to go from here.
Thank you for the help
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with %28c%2Fx%29%2B%28m%2Fa%29=c,

For finding a,
notice a lowest common denominator of xa. Multiply left and right hand members by xa.

xa%28c%2Fx%29%2Bxa%28m%2Fa%29=xac
ac%2Bxm=xac
ac%2Bxm=axc [commutative prop. multip.]
ac-ac%2Bxm=axc-ac
xm=a%28xc-c%29
xm%28xc-c%29%5E%28-1%29=a%28xc-c%29%28xc-c%29%5E%28-1%29, [multiplicative inverse]
xm%2F%28xc-c%29=a%2A1
highlight%28a=xm%2F%28xc-c%29%29