2010 AMC 10B Problems/Problem 8

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Problem

A ticket to a school play cost $x$ dollars, where $x$ is a whole number. A group of 9th graders buys tickets costing a total of $\textdollar 48$, and a group of 10th graders buys tickets costing a total of $\textdollar 64$. How many values for $x$ are possible?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

Solution

We see how many common integer factors $48$ and $64$ share. Of the factors of $48$ - $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$; only $1, 2, 4, 8,$ and $16$ are factors of $64$. So there are $\boxed{\textbf{(E)}\ 5}$ possibilities for the ticket price.

See Also

2010 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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
All AMC 10 Problems and Solutions