Final answer:
By creating two linear equations from the given costs for 4 and 7 hours of rental and solving for the fixed fee and hourly rate, it's determined that the cost to rent the bike for 3 hours is $19.50. However, this answer isn't one of the choices provided, suggesting a possible error in the given options.
Step-by-step explanation:
To solve this problem, we'll use the information given to create two linear equations based on the bike rental costs. From the problem, we know renting a bike for 4 hours costs $24 and for 7 hours costs $37.50. Let's let 'F' represent the fixed fee for renting the bike, and 'H' represent the hourly rate.
Now, we can express these two scenarios with the following equations:
- 4H + F = $24 (renting for 4 hours)
- 7H + F = $37.50 (renting for 7 hours)
To find the values of 'F' and 'H', we can subtract the first equation from the second:
7H + F - (4H + F) = $37.50 - $24
3H = $13.50
Dividing both sides by 3, we get:
H = $4.50
Now we have the hourly rate, we can substitute it back into the first equation to find the fixed fee:
4($4.50) + F = $24
$18 + F = $24
F = $24 - $18
F = $6
The fixed fee for renting the bike is $6, and the hourly rate is $4.50. To find out the cost to rent it for 3 hours:
3($4.50) + $6 = $13.50 + $6
The total cost to rent the bike for 3 hours is $19.50, which is not one of the answer choices provided. Therefore, there might be a mistake in the choices given. However, using the hourly rate and fixed fee figured out, $19.50 is the correct total.