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

Number of Months
Cost ($)
1
52
52
2
74
74
3
96
96

The cost per month is $
.

The initial cost is $
.

1 answer

To analyze the cost structure in the table provided, let's break down the information given:

  1. For 1 month, the total cost is $52.
  2. For 2 months, the total cost is $74.
  3. For 3 months, the total cost is $96.

From this data, we can determine the initial cost and the monthly cost:

Step 1: Find the Initial Cost

The cost appears to have a fixed initial start-up fee followed by a regular monthly fee. We can analyze the differences between the costs for consecutive months to find out the monthly fee.

  • The cost from 1 month to 2 months increases from $52 to $74, which is an increase of $22.
  • The cost from 2 months to 3 months increases from $74 to $96, which is also an increase of $22.

This suggests that the monthly cost is $22.

Step 2: Calculate the Initial Cost

Now that we know the monthly cost, we can calculate the initial cost:

Let \( x \) be the initial cost and \( m \) be the monthly cost. From the data above,

  • For 1 month: \( x + m = 52 \)

    Thus, with \( m = 22 \): \[ x + 22 = 52 \implies x = 52 - 22 = 30 \]

So, the initial cost is $30.

Summary:

  • The cost per month is $22.
  • The initial cost is $30.