Answer:
Longest piece is 21 inches, shorter piece is 13 inches, middle piece is 18.
Step-by-step explanation:
Let x be the longest piece,
∵ the shortest piece is 8 in. shorter than the longest piece,
⇒ Shorter piece ( in inches ) = x - 8 ,
Also, the middle piece is 5 in. longer than the shortest piece,
⇒ Middle piece ( in inches ) = (x - 8) + 5 = x - 3
So, the total length of the sandwich = x + x - 8 + x - 3 = 3x - 11
According to the question,
3x - 11 = 52
3x = 63
⇒ x = 21
Hence, the longest piece is 21 inches, shorter piece is 13 inches, middle piece is 18 inches.