1952 AHSME Problems/Problem 9

Problem

If $m=\frac{cab}{a-b}$ , then $b$ equals:

$\textbf{(A) \ }\frac{m(a-b)}{ca} \qquad \textbf{(B) \ }\frac{cab-ma}{-m} \qquad \textbf{(C) \ }\frac{1}{1+c} \qquad \textbf{(D) \ }\frac{ma}{m+ca} \qquad \textbf{(E) \ }\frac{m+ca}{ma}$

Solution

$m=\frac{cab}{a-b}\implies ma-mb=cab\implies ma=b(m+ac)\implies b=\boxed{\textbf{(D)}\ \frac{ma}{m+ca}}$

1952 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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1952 AHSME Problems/Problem 9

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