SOLUTION: Suppose that a, b, and c are positive integers such that 24/5=a+(1/(b+(1/c+1))). Find all possible values of a, b, and c.

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Question 36007: Suppose that a, b, and c are positive integers such that 24/5=a+(1/(b+(1/c+1))). Find all possible values of a, b, and c.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
A+[1/{B+1/(C+1)}]=A+[1/{(BC+B+1)/(C+1)}]
=A+(C+1)/(BC+B+1)=(ABC+AB+A+C+1)/(BC+B+1)=24/5
TAKING IN SIMPLEST TERMS
BC+B+1=5..OR ...ITS MULTIPLE..
B(C+1)=5-1=4....SINCE A,B,C ARE POSITIVE INTEGERS
FACTORS OF 4 ARE 1,2,4...BY TRIAL WE FIND
FOR B=1 AND C=3...B(C+1)=4...AND N.R. BECOMES
3A+A+A+3+1=24
5A=20
A=4....SATISFIES THE EQN.