For her vacation, Blake wants to rent a bicycle to explore the city. The rental service charges a one-time fee and an additional daily rate for each rental bike. They offer two packages: $32 for a three-day rental, or $41 for a five-day rental. Find the one-time fee and the daily rate for this rental service. Write the linear function representing the relationship between the amount of money spent on bicycle rental and the number of days she rents the bike.
Let's denote the one-time fee as x and the daily rate as y.
Using the information given, we can set up the following system of equations:
3y + x = 32
5y + x = 41
Now we will solve this system of equations, first by subtracting the first equation from the second:
5y + x - (3y + x) = 41 - 32
2y = 9
y = 4.5
Now, we substitute the value of y back into the first equation to solve for x:
3(4.5) + x = 32
13.5 + x = 32
x = 32 - 13.5
x = 18.5
Therefore, the one-time fee is $18.50 and the daily rate is $4.50.
The linear function representing the relationship between the amount of money spent on bicycle rental and the number of days she rents the bike is:
Cost = 4.50d + 18.5
where d is the number of days rented.