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Nagaraj Nanjappa has a party-length sandwich that is 59 inches long and needs to be cut into three pieces. The middle piece will be 5 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?

Answer :

To solve this problem, we need to express the lengths of the three pieces of the sandwich in terms of variables and use the information given to create an equation.

Let's denote:

  • The shortest piece as [tex]x[/tex] inches long.
  • The middle piece as [tex]x + 5[/tex] inches long (since it is 5 inches longer than the shortest piece).
  • The longest piece as [tex]x + 9[/tex] inches long (since the shortest piece is 9 inches shorter than the longest piece).

According to the problem, the total length of the sandwich is 59 inches. Therefore, we can set up the following equation:

[tex]x + (x + 5) + (x + 9) = 59[/tex]

Simplifying the equation:
[tex]x + x + 5 + x + 9 = 59[/tex]
[tex]3x + 14 = 59[/tex]

Subtract 14 from both sides to isolate the terms with [tex]x[/tex]:
[tex]3x = 45[/tex]

Divide both sides by 3 to solve for [tex]x[/tex]:
[tex]x = 15[/tex]

Now that we have [tex]x = 15[/tex], we can find the lengths of each piece:

  1. The shortest piece is [tex]x = 15[/tex] inches.
  2. The middle piece is [tex]x + 5 = 15 + 5 = 20[/tex] inches.
  3. The longest piece is [tex]x + 9 = 15 + 9 = 24[/tex] inches.

Finally, check the total to ensure it sums to 59 inches:
[tex]15 + 20 + 24 = 59[/tex]

Thus, the lengths of the pieces are 15 inches, 20 inches, and 24 inches, respectively.

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