Question

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


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


(2 points)
The cost per month is $

The initial fee is $

Skip to navigation
page 12 of 12

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**.