If a, b, and c are integers satisfying \(a + \frac 1b = \frac{22}{7}\), \(b + \frac 1c = 8\), and abc = 21, then find \(c + \frac 1a\). Express your answer as a common fraction.

If a, b, and c are integers satisfying , , and abc = 21, then find . Express your answer as a common fraction.

\(\{a,b,c\}\subset \{1,3,7\}\ |abc=21\)

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Sorry. Assignment incorrectly written off.

We can solve this by inspection. Logic

If abc = 21 and a + 1/b = 22/7

Then this implies that

a + 1/b = 3 + 1/7

Which implies that a = 3 and b = 7

So

abc =21

(3)(7)(1) = 21

So c = 1

And

c + 1/a = 1 + 1/3