1950 AHSME Problems/Problem 2

Problem

Let $R=gS-4$ . When $S=8$ , $R=16$ . When $S=10$ , $R$ is equal to:

$\textbf{(A)}\ 11\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 20\qquad\textbf{(D)}\ 21\qquad\textbf{(E)}\ \text{None of these}$

Our first procedure is to find the value of $g$ . With the given variables' values, we can see that $8g-4=16$ so $g=\frac{20}{8}=\frac{5}{2}$ .

With that, we can replace $g$ with $\frac{5}{2}$ . When $S=10$ , we can see that $10\times\frac{5}{2}-4=\frac{50}{2}-4=25-4=\boxed{\text{(D) 21}}$ .

1950 AHSC (Problems • Answer Key • Resources)
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