To celebrate a diners anniversary, the owners have made a 40 foot long sandwich. the sandwich is cut into three unequal pieces. the longest piece is three times as long as the middle piece, and the shortest piece is 5 feet shorter than the middle piece. what is the length of the longest piece?

Let x be he length of middle piece.
3x = length of longer piece.
x-5 = length of shortest piece.

x + 3x + x-5 = 40
5x - 5 = 40
5x = 45
x = 45/5
x = 9. ( Size of middle piece )

Given that the longer piece is 3 times the size of middle piece,

Longest piece = 3 x 9 = 27.

Size of longest piece = 27 feet
Size of middle piece = 9 feet
Size of smaller piece = 40 - (27+9)
= 40 - 36
= 4 feet.
Thank you.