2010 AMC 12B Problems/Problem 3

Problem 3

A ticket to a school play cost $x$ dollars, where $x$ is a whole number. A group of 9^th graders buys tickets costing a total of $ $48$ , and a group of 10^th graders buys tickets costing a total of $ $64$ . 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 find the greatest common factor of $48$ and $64$ to be $16$ . The number of factors of $16$ is $5$ which is the answer $(E)$ .

2010 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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
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2010 AMC 12B Problems/Problem 3

Problem 3

Solution

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