AMC10 2003 B

AMC10 2003 B · Q4

AMC10 2003 B · Q4. It mainly tests Fractions, Area & perimeter.

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? [Diagram shows a rectangle divided into regions with side lengths labeled 1, 5, 4, 7, 3, 3, 5, 6]

Rose 在她的矩形花坛的每个矩形区域中种不同种类的花。图中标示了花坛矩形区域的边长，单位为英尺。她每个区域每平方英尺种一朵花。紫菀每朵 1 美元，秋海棠每朵 1.50 美元，美人蕉每朵 2 美元，大丽花每朵 2.50 美元，复活节百合每朵 3 美元。她的花园的最低可能花费是多少美元？[图示一个矩形分为区域，边长标示为 1, 5, 4, 7, 3, 3, 5, 6]

(A) 108 108

(B) 115 115

(D) 144 144

(E) 156 156

Answer

Correct choice: (A)

正确答案：（A）

Solution

To minimize the cost, Rose should place the most expensive flowers in the smallest region, the next most expensive in the second smallest, etc. The areas of the regions are shown in the figure, so the minimal total cost, in dollars, is $(3)(4) + (2.5)(6) + (2)(15) + (1.5)(20) + (1)(21) = 108$.

为了最小化花费，Rose 应该将最贵的花种在最小区域，其次最贵的种在第二小区域，依此类推。图中区域面积已示，最小总花费为 $(3)(4) + (2.5)(6) + (2)(15) + (1.5)(20) + (1)(21) = 108$ 美元。

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