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Source: 2023 AMC12A #10

November 9, 2023
AMCAMC 122023 AMC2023 AMC 12A

Problem Statement

Positive real numbers xx and yy satisfy y3=x2y^3 = x^2 and (y−x)2=4y2(y-x)^2 = 4y^2. What is x+yx+y?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 18<spanclass=′latex−bold′>(C)</span> 24<spanclass=′latex−bold′>(D)</span> 36<spanclass=′latex−bold′>(E)</span> 42<span class='latex-bold'>(A)</span>\ 12 \qquad <span class='latex-bold'>(B)</span>\ 18 \qquad <span class='latex-bold'>(C)</span>\ 24 \qquad <span class='latex-bold'>(D)</span>\ 36 \qquad <span class='latex-bold'>(E)</span>\ 42
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