Can someone please help me find the answer to this problem?

Question

The perimeter of a rectangular lot is 74 feet. The cost of fencing along the two lengths is $1 per foot, and the cost of fencing along the two widths is $3.50 per foot. Find the dimensions of the lot if the total cost of fencing is $159.

Answer 1

L = length

W = width

2*L + 2*W = 74 feet

2*L = 74 - 2W

L = (74 - 2W) / 2

L = 74/2 - 2W/2

L = 37 - W

(2*L*$1/foot) + (2*W*$3.50/feet) = $159

2L + 7W = 159

2(37 - W) + 7W = 159

74 - 2W + 7W = 159

74 + 5W = 159

5W = 159 - 74

5W = 85

W = 17 feet

Since L = 37 - W

L = 37 - 17

L = 20 feet

Verify these answers

2*20*$1/foot + 2*17*$3.50/feet = $159

40 + 119 = 159

159 = 159

Answer 2

Let Length be l and width be w

for perimeter, 2(l+w)=74

divide both sides by 2, l+w=37

                                    l=37-w-----------------(1)

for costing, ($1x l)2+ ($3.5xw)2=$159

                   2l+7w=159

                  2l=159-7w

                  l=(159-7w)/2------------------------(2)

substitute (1) in (2): 37-w=(159-7w)/2

                                74-2w=159-7w

                               7w-2w=159-74

                                 5w=85

                                 w=17

Putting the value of w in equation (1):

                           l=37-w

                           l=20

Answer: The dimensions of the rectangle is 20 feet by 17 feet.