MathDB
2022 A Individual #15

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April 28, 2022
2022 A Individual

Problem Statement

A function f(abc)f(a \tfrac bc) for a simplified mixed fraction abca \tfrac bc returns a+bc\tfrac{a + b}{c}. For instance, f(257)=1f(2 \tfrac 57) = 1 and f(45)=45f(\tfrac45) = \tfrac45. What is the sum of the three smallest positive rational xx where f(x)=29f(x) = \tfrac 29?
<spanclass=′latex−bold′>(A)</span>52<spanclass=′latex−bold′>(B)</span>6827<spanclass=′latex−bold′>(C)</span>239<spanclass=′latex−bold′>(D)</span>7427<spanclass=′latex−bold′>(E)</span>134<span class='latex-bold'>(A) </span>\dfrac52\qquad<span class='latex-bold'>(B) </span>\dfrac{68}{27}\qquad<span class='latex-bold'>(C) </span>\dfrac{23}{9}\qquad<span class='latex-bold'>(D) </span>\dfrac{74}{27}\qquad<span class='latex-bold'>(E) </span>\dfrac{13}4
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