2003 AMC 12B 第 3 题

Question

Rose 把她的长方形花坛中的每个长方形区域种上不同种类的花。图中给出了这些长方形区域的边长，单位为英尺。她在每平方英尺种一株花。紫菀每株

\$1

，秋海棠每株

\$1.50

，美人蕉每株

\$2

，大丽花每株

\$2.50

，复活节百合每株

\$3

。她的花园最少可能花费多少美元？

Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost

\$1

each, begonias

\$1.50

each, cannas

\$2

each, dahlias

\$2.50

each, and Easter lilies

\$3

each. What is the least possible cost, in dollars, for her garden?

108

115

132

144

156

答案：A

知识点：最优化面积

难度评级：1170

小提示：

先从图中求出五个区域的面积

Find the area of each of the five regions from the figure

大提示：

要使总费用最小，把最贵的花种在最小的区域，依此类推

To minimize the total, put the most expensive flower in the smallest region and so on

解答：

五个区域的面积分别为

4

、

6

、

15

、

20

和

21

平方英尺。

为了使费用最小，应把越贵的花种在越小的区域。最小可能费用为

\begin{aligned} &3(4) + 2.5(6) + 2(15) \\ &\quad {}+ 1.5(20) + 1(21) = 108 \end{aligned}\text{。}

因此，正确答案是 A。

The five regions have areas

4,

6,

15,

20,

and

21

square feet.

To minimize the cost, plant the most expensive flowers in the smallest regions. The least possible cost is

\begin{aligned} &3(4) + 2.5(6) + 2(15) \\ &\quad {}+ 1.5(20) + 1(21) = 108. \end{aligned}

Thus, the correct answer is A.

2003 AMC 12B 第 3 题

答案：A

难度评级：1170

小提示：

大提示：

解答：

其他年份的第 3 题