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.