Final answer:
The short piece of molding is 10 feet long, and the long piece is 34 feet long. This was determined by setting up an algebraic equation based on the given relationship between the lengths of the pieces and the total length used.
Step-by-step explanation:
The problem given is a classic algebraic word problem. We need to find the lengths of the short and long pieces of molding used by the carpenter. Let's denote the length of each short piece as x feet. According to the problem, the long piece is 4 feet longer than 3 times the length of the short piece. Therefore, the length of the long piece can be expressed as 3x + 4 feet.
Since there are only two short pieces and one long piece, we can write the total length of molding used as: 2x + (3x + 4) = 54 feet. Simplifying the equation, we get: 5x + 4 = 54. Subtracting 4 from both sides, we get 5x = 50, and by dividing by 5, we find x = 10. So, each short piece is 10 feet long.
Now, let's calculate the long piece: 3x + 4 = 3(10) + 4 = 30 + 4 = 34 feet. Therefore, the length of each short piece is 10 feet and the long piece is 34 feet. The correct answer is A. Short piece: 10 ft, Long piece: 34 ft.