Question 472703
Adding all three of our given statements we obtain x+y+z = 2ax + 2by + 2cz. Matching the x,y,z coefficients, we get 2a = 1, 2b = 1, 2c = 1, so a,b,c = 1/2. Replacing 1/2 into a/(1+a) + b/(1+b) + c/(1+c) yields a sum of 1.