Final answer:
The student is asked to solve for the lengths of two pieces of rope where one piece is 5 feet longer than the other and the total length is 20 feet. Solving the equations from the given conditions, we find that the shorter piece (x) is 7.5 feet and the longer piece (y) is 12.5 feet. Therefore, the correct answer is option (c).
Step-by-step explanation:
The student's question concerns solving a problem where a 20-foot rope is cut into two pieces, with one piece being 5 feet longer than the other. To solve for the lengths of the two pieces of rope, we define two variables: x for the shorter piece and y for the longer piece. According to the problem, y is 5 feet longer than x, so we have the equation y = x + 5. Since the total length of the rope is 20 feet, the two pieces must add up to 20, giving us another equation: x + y = 20.
To find the values of x and y, we substitute the first equation into the second: x + (x + 5) = 20. This simplifies to 2x + 5 = 20. Solving for x, we find x = (20 - 5) / 2, which equals 7.5 feet. Consequently, y would be x + 5, which is 7.5 + 5 = 12.5 feet.
Therefore, option (c) is correct, where x = 7.5 and y = 12.5, representing the shorter and longer pieces of rope, respectively.