Each of A, B and C is a positive real number satisfying this system of equations:
A*B*C = 1, A+1/C =5 and, B+1/A = 29
Find C+1/B
Well, there might be a more direct way to get C + 1/B, but I just solved the three simultaneous equations.
A = 1/BC.
Substituting to eliminate A in the other two equations gives
1/BC + 1/C = 5 and B + BC = 29
Solving both for B gives
B = 1/(5C - 1) and B = 29/(1+C)
Setting them equal and inverting gives
(5C - 1) = (1+C)/29
Then C = 5/24
Then B = 24
Then A = 1/5
So C + 1/B = 5/24 + 1/24 = 1/4
The hard way? (spoiler)
