The table below shows the cost for an online subscription membership with an initial start-up fee charged in the first month. Click Here for Help Video

Question

Number of Months
Cost ($)
1
44
44
2
78
78
3
112
112

The cost per month is $
.

The initial cost is $
.

Answer 1

To determine the cost per month and the initial cost based on the data provided, we can analyze the information in the table for the number of months and the corresponding costs.

From the table:

• For 1 month, the cost is $44.
• For 2 months, the cost is $78.
• For 3 months, the cost is $112.

Now we can calculate the monthly cost:

1. Cost for 1 month:
   Total Cost for 1 month = Initial Cost + Monthly Cost
   \( 44 = Initial Cost + Monthly Cost \)

2. Cost for 2 months:
   Total Cost for 2 months = Initial Cost + 2 * Monthly Cost
   \( 78 = Initial Cost + 2 \times Monthly Cost \)

3. Cost for 3 months:
   Total Cost for 3 months = Initial Cost + 3 * Monthly Cost
   \( 112 = Initial Cost + 3 \times Monthly Cost \)

From the first equation, we can isolate the Initial Cost:

• \( Initial Cost = 44 - Monthly Cost \)

Now we can substitute this expression into the second equation:

\( 78 = (44 - Monthly Cost) + 2 \times Monthly Cost \)
\( 78 = 44 - Monthly Cost + 2 \times Monthly Cost \)
\( 78 = 44 + Monthly Cost \)
\( Monthly Cost = 78 - 44 \)
\( Monthly Cost = 34 \)

Now substituting \( Monthly Cost = 34 \) back into the equation for Initial Cost:

\( Initial Cost = 44 - 34 = 10 \)

So we have the following values:

• The cost per month is $34.
• The initial cost is $10.