Question

If $A + \frac{1}{B + \frac{1}{C - 9}} = \frac{29}{5}$, then the value of $A + B + C$ is

Accepted Answer

C. $\frac{29}{5} = 5 + \frac{4}{5} = 5 + \frac{1}{5/4} = 5 + \frac{1}{1 + 1/4}$. So $A = 5$, $B = 1$, and $C - 9 = 4 \implies C = 13$. Then $A + B + C = 5 + 1 + 13 = 19$.

Continued Fraction Algebra

Explanation

Practise this under exam conditions