Skip to main content

2003 AMC 10B Problem 4

Problem 4 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?

Answer choices

Show solution

Solution

The five regions have areas 4,4, 6,6, 15,15, 20,20, and 2121 square feet. Cost is minimized by placing the most expensive flower in the smallest region, so the total is (3)(4)+(2.5)(6)+(2)(15)+(1.5)(20)+(1)(21)=108. \begin{gathered} (3)(4)+(2.5)(6)+(2)(15) \\ {}+(1.5)(20)+(1)(21) \\ = 108. \end{gathered} Thus, the correct answer is A.
AoPS wiki

Tagged: area · optimization · pairing and grouping

More practice