A water park charges a rental fee plus an hourly fee for inflatable inner tubes. The total costs of 3, 4, and 5 hours are $8.00, $8.75, and $9.50, respectively.

Question

Make a table or draw a graph to determine the rental fee and the hourly fee the water park charges.

What is the cost of the hourly fee?

What is the cost of the rental fee?

Answer 1

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:

1. For 3 hours:
   \[ r + 3h = 8.00 \]

2. For 4 hours:
   \[ r + 4h = 8.75 \]

3. For 5 hours:
   \[ r + 5h = 9.50 \]

Now we can set up the equations:

1. \( r + 3h = 8.00 \) (Equation 1)
2. \( r + 4h = 8.75 \) (Equation 2)
3. \( r + 5h = 9.50 \) (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