If-97-19-a-1-b-1-c-where-a-b-and-c-are-positive-integers-then-what-is-the-sum-of-a-b-and-c-

Question Number 112804 by Aina Samuel Temidayo last updated on 09/Sep/20

If \frac{97}{19} = a + \frac{1}{b + \frac{1}{c}}, where a, b and c are

positive integers, then what is the sum

of a, b and c ?

Answered by nimnim last updated on 09/Sep/20

\frac{97}{19} = 5 + \frac{2}{19} = 5 + \frac{1}{\frac{19}{2}} = 5 + \frac{1}{9 + \frac{1}{2}}

\Rightarrow a = 5, b = 9, c = 2

∴ (a + b + c) = 16 ★

Commented by Aina Samuel Temidayo last updated on 09/Sep/20

Thanks .