Final answer:
John rented the car for 7 days. This was determined by setting up a linear equation with the total cost of $242.50, subtracting the flat rate of $50, and dividing the remainder by the daily rate of $27.50.
Step-by-step explanation:
To determine how many days John rented the car, we first need to consider the flat rate and daily charge. According to the problem, John paid a flat rate of $50 and a daily rate of $27.50. The total cost of the car rental was $242.50. We can set up a linear equation to find the number of days John rented the car.
Let d represent the number of rental days. The total cost (T) of renting the car can be calculated using the following formula:
T = flat rate + (daily rate × number of days)
Which translates to:
T = $50 + $27.50d
Since the total cost is $242.50, we can substitute T with 242.50 and solve for d:
242.50 = $50 + $27.50d
To solve for d, we first subtract the flat rate from the total cost:
242.50 - $50 = $27.50d
Which simplifies to:
192.50 = $27.50d
Now, we divide both sides by the daily rate to find the number of days:
d = 192.50 ÷ $27.50
Which gives us:
d = 7
Therefore, John rented the car for 7 days.