Problema Solution
A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 56 feet. If the material used to build the pen is $1.50 per foot for the longer sides and $2.50 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.
Answer provided by our tutors
let
l = the length of the pen
w = the width of the pen
the pen is 3 times as long as it is wide
l = 3w
the perimeter is 56 feet
2(l + w) = 56 divide both sides by 2
l + w = 28
by solving the system of equations
l = 3w
l + w = 28
we find
l = 21 ft
w = 7 ft
click here to see the step by step solution of the system of equations
the money paid for the longer sides is: 1.50*2*l = 1.50*2*21 = $62
the money paid for the shorter sides is: 2.50*2*w = 2.50*2*7 = $35
the total cost to build the pen is 62 + 35 = $97.