The table below shows the cost for a movie theater membership with an initial start-up fee charged in the first month. Help Video

Question

Number of Months Cost ($)
1 75
2 105
3 135


(2 points)
The cost per month is $

The initial fee is $

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Answer 1

To find the cost per month and the initial fee, we can use the information provided in the table.

Using the table:

• For 1 month: Cost = $75
• For 2 months: Cost = $105
• For 3 months: Cost = $135

Step 1: Determine the initial fee and monthly cost

Let:

• \( F \) = initial fee
• \( C \) = monthly cost

From the data for 1 month: \[ F + C = 75 \tag{1} \]

From the data for 2 months: \[ F + 2C = 105 \tag{2} \]

From the data for 3 months: \[ F + 3C = 135 \tag{3} \]

Step 2: Solve the equations

To find the monthly cost, we can subtract equation (1) from equation (2):

\[ (F + 2C) - (F + C) = 105 - 75 \] \[ C = 30 \text{ (cost per month)} \]

Now, substitute \( C \) back into equation (1) to find \( F \):

\[ F + 30 = 75 \] \[ F = 75 - 30 = 45 \text{ (initial fee)} \]

Summary:

• The cost per month is $30.
• The initial fee is $45.