Difference between revisions of "1953 AHSME Problems/Problem 6"

Problem 6

Charles has $5q + 1$ quarters and Richard has $q + 5$ quarters. The difference in their money in dimes is:

$\textbf{(A)}\ 10(q - 1) \qquad \textbf{(B)}\ \frac {2}{5}(4q - 4) \qquad \textbf{(C)}\ \frac {2}{5}(q - 1) \\ \textbf{(D)}\ \frac{5}{2}(q-1)\qquad \textbf{(E)}\ \text{none of these}$

Solution

$5q+1-q-5\implies 4p-4\implies\frac{4(p-1)}{10}\implies\frac{2(p-1)}{5}$, $\fbox{D}$ If Charles has $5q +1$ quarters and Richard has $q+5$ quarters, then the difference between them is $4q-4$ quarters. Converting quarters to dimes, the difference between them is $\frac{5}{2}\cdot (4)(q-1)$, or $10(q-1)$ dimes, $\implies \fbox{A}$

See Also

 1953 AHSC (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 All AHSME Problems and Solutions

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