Question

The table below shows the cost for an online subscription membership with an initial start-up fee charged in the first month.
Number of Months cost($)
1. 40.
2. 60.
3. 80.
the initial cost is $_____.

Answer 1

To determine the initial cost, we can analyze the cost for the subscription for the different number of months provided in the table.

Let's assume the initial start-up fee is represented as \( C \) and the monthly subscription fee is \( M \).

From the data:
1. For 1 month, the cost is represented as:
\[
C + M = 40
\]

2. For 2 months, the cost is:
\[
C + 2M = 60
\]

3. For 3 months, the cost is:
\[
C + 3M = 80
\]

Now, we can set up a system of equations based on these relations.

From the first equation:
1. \( C + M = 40 \) → (i)

From the second equation:
2. \( C + 2M = 60 \) → (ii)

From the third equation:
3. \( C + 3M = 80 \) → (iii)

Now, we can solve for \( C \) and \( M \) using these equations.

Subtract equation (i) from equation (ii):
\[
(C + 2M) - (C + M) = 60 - 40
\]
\[
M = 20
\]

Now that we have \( M \), we can substitute it back into equation (i) to find \( C \):
\[
C + 20 = 40
\]
\[
C = 40 - 20 = 20
\]

Thus, the initial cost (start-up fee) is **$20**.