Answer:
The three pieces should be 13 , 19 , 22 inches
Step-by-step explanation:
* Lets study the information to solve the problem
- The length of the sandwich is 54 in
- The sandwich will cut into three pieces
- The middle piece is 6 inches longer than the shortest piece
- The shortest piece is 9 inches shorter than the longest piece
* Lets change the above statements to equations
∵ The shortest piece is common in the two statements
∴ Let the length of the shortest piece is x ⇒ (1)
∵ The middle piece is 6 inches longer than the shortest piece
∴ The length of the middle piece = x + 6 ⇒ (2)
∵ The shortest piece is 9 inches shorter than the longest piece
∴ The longest piece is 9 inches longer than the shortest piece
∴ The longest piece = x + 9 ⇒ (3)
∵ the length of the three pieces = 54 inches
- Add the length of the three pieces and equate them by 54
∴ Add (1) , (2) , (3)
∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms
∴ 3x + 15 = 54 ⇒ subtract 15 from both sides
∴ 3x = 39 ⇒ divide both sides by 3
∴ x = 13
* The length of the shortest piece is 13 inches
∵ The length of the middle piece = x + 6
∴ The length of the middle piece = 13 + 6 = 19 inches
* The length of the middle piece is 19 inches
∵ The length of the longest piece = x + 9
∴ The length of the longest piece = 13 + 9 = 22 inches
* The length of the longest piece is 22 inches
* The lengths of the three pieces are 13 , 19 , 22 inches
