Sunia is looking to join a new gym and is analyzing how much money it will cost her to be a member. The gym has a one-time startup fee of

Question

and costs
per month to maintain membership. From this information, Sunia develops the equation
to represent the total cost,
, of being a member for
months.

PART A

Complete the table to find six solutions to Sunia's equation.

Months (
) Total Cost (
)
0
1
2
3
4
5

Answer 1

To develop the equation representing the total cost \( C \) of being a member for \( m \) months, we need to consider both the one-time startup fee and the monthly maintenance cost.

Let’s assume:

• The one-time startup fee is \( S \).
• The monthly cost is \( P \).

The equation for the total cost can be expressed as:

\[ C = S + P \cdot m \]

Now, if we fill out the table for \( m = 0, 1, 2, 3, 4, 5 \), we need the specific values for \( S \) and \( P \) to provide a numerical solution. However, I can demonstrate how to fill out the table with placeholders.

Assume:

• Startup fee \( S = 100 \) (for example)
• Monthly cost \( P = 20 \) (for example)

Using these values, the equation becomes:

\[ C = 100 + 20m \]

Now, let’s fill out the table:

| Months (\( m \)) | Total Cost (\( C \)) | |-------------------|----------------------| | 0 | \( 100 + 20 \times 0 = 100 \) | | 1 | \( 100 + 20 \times 1 = 120 \) | | 2 | \( 100 + 20 \times 2 = 140 \) | | 3 | \( 100 + 20 \times 3 = 160 \) | | 4 | \( 100 + 20 \times 4 = 180 \) | | 5 | \( 100 + 20 \times 5 = 200 \) |

Thus, the completed table with this specific example would look like:

| Months (\( m \)) | Total Cost (\( C \)) | |-------------------|----------------------| | 0 | 100 | | 1 | 120 | | 2 | 140 | | 3 | 160 | | 4 | 180 | | 5 | 200 |

Feel free to replace \( S \) and \( P \) with the actual values to get specific total costs.