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.

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?

1 answer

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