Final answer:
The equation 5x + 8 - 7x = -4x + 1 has one unique solution, which is x = -7/2. To determine the hours of repair in the plumber scenario, use the equation y = 65 + 25x; solving for the given total bill of $115, the repair took 2 hours.
Step-by-step explanation:
The first part of the student's question asks about the number of solutions for the equation 5x + 8 - 7x = -4x + 1. To determine the answer, we simplify the equation by combining like terms to get -2x + 8 = -4x + 1. Adding 4x to both sides yields 2x + 8 = 1. Then, subtracting 8 from both sides gives 2x = -7, and dividing both sides by 2 yields x = -7/2. Hence, the equation has one unique solution.
For the second scenario, we want to find out how many hours the repair took if the plumber charges a flat fee of $65 plus $25 an hour and the total bill was $115. We can set up the equation 65 + 25h = 115, where h represents the number of hours worked. Subtracting 65 from both sides gives us 25h = 50, and dividing by 25 yields h = 2. Thus, the repair took 2 hours.
The equation that can be used to solve the plumber's charge problem is y = 65 + 25x, where y represents the total bill and x represents the number of hours worked.