AMC12 2008 B

AMC12 2008 B · Q5

AMC12 2008 B · Q5. It mainly tests Basic counting (rules of product/sum), Parity (odd/even).

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?

一个班级筹集了 $50$ 美元，为住院的同学买花。玫瑰每朵 $3$ 美元，康乃馨每朵 $2$ 美元。不使用其他花。恰好花 $50$ 美元可以购买多少种不同的花束？

(A) 1 1

(B) 7 7

(D) 16 16

(E) 17 17

Answer

Correct choice: (C)

正确答案：（C）

Solution

The class could send $25$ carnations and no roses, $22$ 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), $\Rightarrow \boxed{C}$

该班可以送 $25$ 朵康乃馨且不买玫瑰，或 $22$ 朵康乃馨和 $2$ 朵玫瑰，或 $19$ 朵康乃馨和 $4$ 朵玫瑰，依此类推，直到 $1$ 朵康乃馨和 $16$ 朵玫瑰。共有 9 种可能（玫瑰从 0 到 16，每次增加 2），$\Rightarrow \boxed{C}$。

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