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2003 AMC 12B Problem 3

Problem 3 of 25EasierGeometryProblem-Solving Techniques

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\$1 each, begonias $1.50\$1.50 each, cannas $2\$2 each, dahlias $2.50\$2.50 each, and Easter lilies $3\$3 each. What is the least possible cost, in dollars, for her garden?

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Solution

The five regions have areas 4,4, 6,6, 15,15, 20,20, and 2121 square feet. To minimize the cost, plant the most expensive flowers in the smallest regions. The least possible cost is 3(4)+2.5(6)+2(15)+1.5(20)+1(21)=108. \begin{aligned} &3(4) + 2.5(6) + 2(15) \\ &\quad {}+ 1.5(20) + 1(21) = 108. \end{aligned} Thus, the correct answer is A.
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Tagged: optimization · area

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