Problem

2017 Fermat Problem 23

Sylvia chose positive integers $a$ , $b$ and $c$ .

Peter determined the value of $a + \dfrac{b}{c}$ and got an answer of $101$ .

Paul determined the value of $\dfrac{a}{c} + b$ and got an answer of $68$ .

Mary determined the value of $\dfrac{a+b}{c}$ and got an answer of $k$ .

The value of $k$ is

$\textbf{(A)}\ 13\quad$ $\textbf{(B)}\ 168\quad$ $\textbf{(C)}\ 152\quad$ $\textbf{(D)}\ 12\quad$ $\textbf{(E)}\ 169$

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.

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Difficulty —

Category: Fermat
Points: 3
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