Question

Nagaraj has a​ party-length sandwich that is 61 inches long and is to be cut into three pieces. The middle piece will be 4 inches longer than the shortest​ piece, and the shortest piece will be 9 inches shorter than the longest piece. How long will the pieces​ be?
The length of the shortest piece is
nothing inches. The length of the medium piece is
nothing inches. The length of the longest piece is
nothing inches.

Answer 1

Answer: The length of the shortest piece is 16 inches

The length of the medium piece is

20 inches

The length of the longest piece is 25 inches.

Step-by-step explanation:

Total length of the party sandwich is 61 inches. This length is to be cut into three different pieces.

Let x= the size of the longest piece.

Let y = the size of the medium piece.

Let z = the size of the shortest piece.

The middle piece will be 4 inches longer than the shortest​ piece. This means that

y = z + 4 - - - - - - 1

The shortest piece will be 9 inches shorter than the longest piece. This means that

x = z +9 - - - - - - -2

Since total length of the party sandwich is 61 inches, it means that

x + y + z = 61 - - - - - - -3

We will substitute equation 1 and equation 2 into equation 3. It becomes

z + 9 + z + 4 + z = 61

13 + 3z = 61

3z = 61 - 13 = 48

z = 48/3 = 16

y = z + 4 = 16 + 4

y = 20

x = z + 9 = 16 + 9

x = 25