1960 AHSME Problems/Problem 29

Problem

Five times $A$ 's money added to $B$ 's money is more than $$51.00$ . Three times $A$ 's money minus $B$ 's money is $$21.00$ . If $a$ represents $A$ 's money in dollars and $b$ represents $B$ 's money in dollars, then:

$\textbf{(A)}\ a>9, b>6 \qquad \textbf{(B)}\ a>9, b<6 \qquad \textbf{(C)}\ a>9, b=6\qquad \textbf{(D)}\ a>9, \text{but we can put no bounds on} \text{ } b\qquad \textbf{(E)}\ 2a=3b$

Solution

Use math symbols to write an equation and an inequality based on the conditions in the problem. $5a+b>51$ $3a-b=21$ From the second equation, $b = 3a-21$ and $a = 7 + b/3$ .

Substituting $b$ in the inequality results in $5a + 3a - 21 > 51$ $8a > 72$ $a > 9$

Substituting $a$ in the inequality results in $35 + \frac{5b}{3} + b > 51$ $35 + \frac{8b}{3} > 51$ $\frac{8b}{3} > 16$ $b > 6$

The answer is $\boxed{\textbf{(A)}}$ .

1960 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 28	Followed by Problem 30
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1960 AHSME Problems/Problem 29

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