SOLUTION: Find the sum of a, b and c if: a + 1/(b+1/c) = 37/16

Question 1096548: Find the sum of a, b and c if: a + 1/(b+1/c) = 37/16
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

There are an infinite number of solutions if there are no restrictions on the values of a, b, and c. So I will assume the problem requires the values to be positive integers. In that case....

Since a, b, and c have to be positive integers, there are only two possibilities:
(1) and ; or
(2) and

Looking for a solution for case (1)...

Clearly there are no positive integer values for b that produce positive integer values for c. So there are no solutions for this case.

Looking for a solution for case (2)...

There is exactly one positive integer value for b that produces a positive integer value for c: b=3 gives c=5.

So there is a unique solution to the problem in positive integers:
a=2;
b=3;
c=5

CHECK:

The answer to the problem is then a+b+c = 10.
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