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Money Givers A,B,C

Source: AHSME 1963 Problem 23

January 10, 2014
algebrasystem of equationsAMC

Problem Statement

AA gives BB as many cents as BB has and CC as many cents as CC has. Similarly, BB then gives AA and CC as many cents as each then has. CC, similarly, then gives AA and BB as many cents as each then has. If each finally has 1616 cents, with how many cents does AA start?
<spanclass=latexbold>(A)</span> 24<spanclass=latexbold>(B)</span> 26<spanclass=latexbold>(C)</span> 28<spanclass=latexbold>(D)</span> 30<spanclass=latexbold>(E)</span> 32<span class='latex-bold'>(A)</span>\ 24 \qquad <span class='latex-bold'>(B)</span>\ 26\qquad <span class='latex-bold'>(C)</span>\ 28 \qquad <span class='latex-bold'>(D)</span>\ 30 \qquad <span class='latex-bold'>(E)</span>\ 32