To find the rental fee and the hourly fee for the inflatable inner tubes, we can set up a system of equations based on the information provided. Let's denote:
- \( r \): rental fee (fixed cost)
- \( h \): hourly fee (cost per hour)
We are given the following costs for 3, 4, and 5 hours:
-
For 3 hours:
\[ r + 3h = 8.00 \] -
For 4 hours:
\[ r + 4h = 8.75 \] -
For 5 hours:
\[ r + 5h = 9.50 \]
Now we can set up the equations:
- \( r + 3h = 8.00 \) (Equation 1)
- \( r + 4h = 8.75 \) (Equation 2)
- \( r + 5h = 9.50 \) (Equation 3)
Now, we can subtract Equation 1 from Equation 2 to eliminate \( r \):
\[ (r + 4h) - (r + 3h) = 8.75 - 8.00 \]
This simplifies to:
\[ h = 0.75 \]
Next, subtract Equation 2 from Equation 3:
\[ (r + 5h) - (r + 4h) = 9.50 - 8.75 \]
This simplifies to:
\[ h = 0.75 \]
Now that we know \( h = 0.75 \) (the hourly fee), we can substitute this value back into one of our original equations to find \( r \). We'll use Equation 1:
\[ r + 3(0.75) = 8.00 \] \[ r + 2.25 = 8.00 \] \[ r = 8.00 - 2.25 \] \[ r = 5.75 \]
Now we have:
- Hourly fee (\( h \)): $0.75
- Rental fee (\( r \)): $5.75
Summary:
Hourly Fee: $0.75
Rental Fee: $5.75