A boy purchased a party-length sandwich 50 in. long. He wants to cut it into three pieces so that the middle piece is 6 in. longer than the shortest piece and the shortest piece is 8 in. shorter than the longest piece. How long should the three pieces be?

The length of shortest piece is 12 inches and length of middle piece is 18 inches and length of longest piece is 20 inches

Solution:

Let, "x" be the shortest piece

The middle piece is 6 in. longer than the shortest piece

Middle piece = 6 + x

The shortest piece is 8 in. shorter than the longest piece

Longest piece = 8 + x

A boy purchased a party-length sandwich 50 in. long

Therefore, total length = 50

Shortest piece + Middle piece + Longest piece = 50

x + 6 + x + 8 + x = 50

14 + 3x = 50

3x = 50 - 14

3x = 36

Divide both the sides by 3

x = 12

Therefore,

shortest piece = 12

middle piece = 6 + x = 6 + 12 = 18

longest piece = 8 + x = 8 + 12 = 20

Thus, length of shortest piece is 12 inches and length of middle piece is 18 inches and length of longest piece is 20 inches