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

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, $\implies \fbox{A}$

Note that $q$ does not stand for the number of quarters that they have.

See Also

1953 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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