Final answer:
The shorter piece is 7 feet long, and the longer piece is 16 feet long.
Step-by-step explanation:
To solve this problem, let's represent the length of the shorter piece as x. According to the given information, the longer piece is 2 feet longer than twice the length of the shorter piece, so we can represent the longer piece as 2x + 2.
We know that the total length of the molding used is 30 feet, so we can set up the equation:
x + x + 2x + 2 = 30
Combining like terms, we have 4x + 2 = 30.
Subtracting 2 from both sides gives 4x = 28.
Dividing both sides by 4, we find x = 7.
Therefore, the shorter piece is 7 feet long, and the longer piece is 2(7) + 2 = 16 feet long.