Final answer:
The hourly fee charged by the water park is $0.75, and the rental fee is $5.75. These values were obtained by setting up a system of linear equations based on the cost for different rental hours provided and then solving for the hourly fee (H) and rental fee (R).
Step-by-step explanation:
To determine the water park's rental fee and hourly fee for inflatable inner tubes, we will use the given data to set up a system of linear equations. Let R be the rental fee and H be the hourly fee. The total cost for renting the tubes for 3 hours is $8.00, for 4 hours it is $8.75, and for 5 hours it's $9.50. These scenarios give us three equations:
- R + 3H = $8.00
- R + 4H = $8.75
- R + 5H = $9.50
If we subtract the first equation from the second one, we eliminate R and solve for H:
(R + 4H) - (R + 3H) = $8.75 - $8.00
R + 4H - R - 3H = $0.75
H = $0.75
The hourly fee is $0.75.
Now that we have H, we can plug it back into the first equation to solve for R:
R + 3($0.75) = $8.00
R + $2.25 = $8.00
R = $8.00 - $2.25
R = $5.75
The rental fee is $5.75.