A boy purchased (bought) a party-length sandwich 50 in . long. He wants to cut it into three pieces so that the middle piece is 5 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?

Let the length of the shortest piece be \( x \) inches. Then the longest piece would be \( x + 9 \) inches, and the middle piece would be \( x + 5 \) inches. According to the problem, the total length of the sandwich is 50 inches. So, we can set up the equation: \[ x + (x + 5) + (x + 9) = 50 \] Simplifying this, we get: \[ 3x + 14 = 50 \] Subtracting 14 from both sides gives: \[ 3x = 36 \] Dividing by 3 results in: \[ x = 12 \] Now we can find the lengths of the three pieces: - Shortest piece: \( x = 12 \) inches - Longest piece: \( x + 9 = 12 + 9 = 21 \) inches - Middle piece: \( x + 5 = 12 + 5 = 17 \) inches Thus, the lengths of the three pieces should be 12 inches, 17 inches, and 21 inches.