Question

A man wishes to to fence a rectangular lot which ensures 80 feet by 140 feet. The fence along the front (80 ft) of the lot costs one and one-half times as much per foot as that along the three other sides. If the total cost of the fence is $960, find the cost per foot of each type of fence.

Answer 1

Given,total cost(P) = $960

Let cost of 1 foot fence = x

length of fence costing x (P1) = l + 2*b

here, l = length of back fence = 80 ft

b = length of side fence = 140 ft

P1 = 80 + 2*140 = 360 ft

length of fence costing 1.5*x (P2) = l

here, l = length of front fence = 80 ft

P2 = 80 ft

So, total cost(P) = P1*x + P2*(1.5*x)

P = 360*x + 80*1.5*x

960 = (360 + 1.5*80)*x

x = 960/(360 + 1.5*80)

x = $2 = cost of per foot in fencing of sides and back

Cost of per foot in fencing of front = 1.5*x = 1.5*2

Cost of per foot in fencing of front = $3

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