A boy purchased (bought) a party-length sandwich 54 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 9 in. shorter than the longest piece. How long should the three pieces be?

Question

Mathematics

Alicia

18 September, 15:17

A boy purchased (bought) a party-length sandwich 54 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 9 in. shorter than the longest piece. How long should the three pieces be?

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Answers (2)

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Brynn Maxwell · Answer 1

length of shortest piece = 13 in

length of middle piece = 19 in

length of longest piece = 22 in

Step-by-step explanation:

Total length of sandwich = 54 inch

Let shortest piece = x

Middle piece = x+6

Longest piece = x+9

Add this pieces will make complete sandwich

x + (x+6) + (x+9) = 54

Solving

x+x+6+x+9 = 54

Combining like terms

x+x+x+6+9 = 54

3x + 15 = 54

3x = 54 - 15

3x = 39

x = 13

So, length of shortest piece = x = 13 in

length of middle piece = x+6 = 13+6 = 19 in

length of longest piece = x+9 = 13+9 = 22 in

Gilbert · Answer 2

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