A rectangular lot whose perimeter is 360 feet is fenced along three sides. An expensive fencing along the lot's length costs $25 per foot

Question

, and an inexpensive fencing along the two side widths costs only $6 per foot. The total cost of the fencing along the three sides comes to $3590. What are the lot's dimensions?

Answer 1

this is a 2 equations in 2 unknowns problem

Equation 1

assuming the length is L and width is W, then

2L + 2W = 360

Equation 2

cost of the fence along the fence is $25* L = 25L

cost of the fence along the two widths is $6 * 2W = 12W

cost of the 3 sides = $3590 = 25L + 12W

Solve

from equation 1, and by diving by 2, L = 180 - W

substitute for L in equation 2, then

3590 = 25 (180 - W) + 12W

3590 = 4500 - 25W + 12W

13W = 910

W = 70 feet

L = 180 - (70) = 110 feet

Length is 110 feet and Width is 70 feet