2009 Fermat Problem 21

At Matilda's birthday party, the ratio of people who ate ice cream to people who ate cake was 3 : 2. People who ate both ice cream and cake were included in both categories. If 120 people were at the party, what is the maximum number of people who could have eaten both ice cream and cake?

\textbf{(A)}\ 24\quad \textbf{(B)}\ 30\quad \textbf{(C)}\ 48\quad \textbf{(D)}\ 80\quad \textbf{(E)}\ 72

If there are no answer choices shown, enter a numerical answer.

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