Alivestock pen is built in the shape of a rectangle that is twice as long as it is wide. the perimeter is 48 feet. if the material used to build the pen is $1.85 per foot for the longer sides and $2.35 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.

Wow!  This has to handled one step at a time.
Step 1). Find the actual dimensions of the pen.
Step 2). Decide the total amount on longer sides
and the total amount on shorter sides.
Step 3). Work out the costs.

Dimensions of the pen:
"Twice as long as it is wide".
Width = W feet
Length = 2W feet
Perimeter = W + 2W + W + 2W = 6W = 48 feet
Width = W = 8 feet
Length = 2W = 16 feet

Amount on long sides and short sides:
The longer sides are 16 feet.
There are 2 of them.
Total mount on longer sides = 32 feet.

The shorter sides are 8 feet.
There are 2 of them.
Total amount on shorter sides = 16 feet.

Costs:
Longer sides: (32 feet) x ($1.85 per feet) = $59.20
Shorter sides: (16 feet) x ($2.35 per foot) =  $37.60
Total cost of material to build the pen = $96.80