A rectangular garden is to be surrounded on three sides by a fence costing $5 per foot and on one side by a stone wall costing $15 per foot. Let x be the length of the side with the stone wall, and let y be the length of each of the other three sides. Express the cost of enclosing the garden as a function of two variables.
A) C(x, y) = (15x)(5y)
B) C(x, y) = 15x + 5y
C) C(x, y) = (20x)(10y)
D) C(x, y) = 15x + 15y
E) none of these

Question

Quizplus · Accepted Answer

The length of the fence required for three sides (which cost $5 per foot) is 3y. Therefore, the cost of the fence is 3y * 5 = 15y.

The length of the wall required for one side (which costs $15 per foot) is x. Therefore, the cost of the wall is x * 15 = 15x.

The total cost of enclosing the garden is the sum of the cost of the fence and the wall, which is 15y + 15x. Therefore, the best choice for the function is D.

A Rectangular Garden Is to Be Surrounded on Three Sides