AMC10 2008 B

AMC10 2008 B · Q8

AMC10 2008 B · Q8. It mainly tests Money / coins, Parity (odd/even).

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

一个班级收集了 $50 来为住院的同学买花。玫瑰每朵 $3，康乃馨每朵 $2。不使用其他花。有多少种不同的花束可以用恰好 $50 购买？

(A) 1 1

(B) 7 7

(D) 16 16

(E) 17 17

Answer

Correct choice: (C)

正确答案：（C）

Solution

The total number of dollars spent is the even number 50, so the number of roses purchased must also be even. In addition, the number of roses purchased cannot exceed $\frac{50}{3}$. Therefore the number of roses purchased must be one of the even integers between 0 and 16, inclusive. This gives 9 possibilities for the number of bouquets.

总花费是偶数 50，因此购买的玫瑰数量必须是偶数。此外，购买的玫瑰数量不能超过 $\frac{50}{3}$。因此玫瑰数量必须是 0 到 16（包含）之间的偶整数。这给出 9 种花束的可能性。

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