2003 AMC 10B Problem 4

Question

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

Answer: A

Concepts:area optimization pairing and grouping

Difficulty rating: 1070

Small hint:

Find the area of each of the five regions first

Big hint:

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

Solution:

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.