a boy purchased a party length sandwich 57 in long . he wants to cut it in to 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 ?
Let's assume that the shortest piece is x inches long.
According to the given information, the middle piece is 6 inches longer than the shortest piece, so its length would be x + 6 inches.
The longest piece is 9 inches longer than the shortest piece, so its length would be x + 9 inches.
To find the total length of the sandwich, we add up the lengths of all three pieces:
x + (x + 6) + (x + 9) = 57
Combining like terms, we have:
3x + 15 = 57
Subtracting 15 from both sides, we get:
3x = 42
Dividing both sides by 3, we find:
x = 14
Therefore, the shortest piece is 14 inches long.
The middle piece is 6 inches longer, so it would be:
14 + 6 = 20 inches long.
The longest piece is 9 inches longer, so it would be:
14 + 9 = 23 inches long.
Thus, the three pieces should be 14 inches, 20 inches, and 23 inches long.