Question

罗斯用不同种类的花填满她的长方形花坛中的每个长方形区域。图中给出了这些长方形区域的边长，单位为英尺。她在每个区域每平方英尺种一朵花。紫菀每朵 $\$1$ ，秋海棠每朵 $\$1.50$ ，美人蕉每朵 $\$2$ ，大丽花每朵 $\$2.50$ ，复活节百合每朵 $\$3$ 。她的花园最少可能花多少钱？

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：面积最优化配对与分组

难度评级：1070

小提示：

先求出五个区域各自的面积。

Find the area of each of the five regions first

大提示：

为了使费用最小，把最贵的花种在最小的区域。

To minimize cost, plant the most expensive flower in the smallest region

解答：

五个区域的面积分别为 $4$ 、 $6$ 、 $15$ 、 $20$ 和 $21$ 平方英尺。

要使费用最小，应把最贵的花种在最小的区域，所以总费用为 $\begin{gathered} (3)(4)+(2.5)(6)+(2)(15) \\ {}+(1.5)(20)+(1)(21) \\ = 108 \end{gathered}\text{。}$

所以正确答案是 A。

The five regions have areas $4,$ $6,$ $15,$ $20,$ and $21$ square feet.

Cost is minimized by placing the most expensive flower in the smallest region, so the total is $\begin{gathered} (3)(4)+(2.5)(6)+(2)(15) \\ {}+(1.5)(20)+(1)(21) \\ = 108. \end{gathered}$

Thus, the correct answer is A.

2003 AMC 10B 第 4 题

答案：A

难度评级：1070

小提示：

大提示：

解答：

其他年份的第 4 题