2008 AMC 12B Problems/Problem 5

Problem 5

A class collects $50$ dollars to buy flowers for a classmate who is in the hospital. Roses cost $3$ dollars each, and carnations cost $2$ dollars each. No other flowers are to be used. How many different bouquets could be purchased for exactly $50$ dollars?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 7 \qquad \textbf{(C)}\ 9 \qquad \textbf{(D)}\ 16 \qquad \textbf{(E)}\ 17$

Solution

The class could send just carnations (25 of them). They could also send 22 carnations and 2 roses, 19 carnations and 4 roses, and so on, down to 1 carnation and 16 roses. There are 9 total possibilities (from 0 to 16 roses, incrementing by 2 at each step), which is answer choice C.

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2008 AMC 12B Problems/Problem 5

Problem 5

Solution