AT&T offers premium internet service for $39.95 plus a one-time setup fee. The total cost for setup and 6 months of service is $264.70. Which linear equation represents the total c... AT&T offers premium internet service for $39.95 plus a one-time setup fee. The total cost for setup and 6 months of service is $264.70. Which linear equation represents the total cost of service?
Understand the Problem
The question is asking which linear equation represents the total cost of AT&T's internet service, considering a monthly fee and a one-time setup fee, given a specific total cost for setup and six months of service.
Answer
The equation representing the total cost is $y - 264.70 = 39.95(x - 6)$.
Answer for screen readers
The linear equation that represents the total cost of service is: $$ y - 264.70 = 39.95(x - 6) $$
Steps to Solve
- Define the Variables
Let:
- ( y ) be the total cost of the internet service for 6 months.
- ( x ) be the number of months of service (in this case, ( x = 6 )).
- The monthly service fee is $39.95.
- The one-time setup fee is ( S ) (unknown).
- Write the Total Cost Equation
The total cost equation can be expressed as: $$ y = S + 39.95 \times x $$
Substituting ( x ) with 6 (since it's for 6 months): $$ y = S + 39.95 \times 6 $$
- Substitute the Known Total Cost
You know that the total cost ( y ) for setup and 6 months of service is $264.70: $$ 264.70 = S + 39.95 \times 6 $$
- Calculate the Monthly Costs for 6 Months
Calculate ( 39.95 \times 6 ): $$ 39.95 \times 6 = 239.70 $$
Therefore, the equation becomes: $$ 264.70 = S + 239.70 $$
- Solve for Setup Fee ( S )
To find the setup fee: $$ S = 264.70 - 239.70 $$
This gives: $$ S = 25 $$
Thus, the total cost equation is: $$ y = 25 + 39.95 \times x $$
- Rearranging the Final Equation
This can be rearranged as: $$ y - 25 = 39.95 \times x $$
Substituting ( x ) back for ( (x - 6) ) yields: $$ y - 264.70 = 39.95(x - 6) $$
The linear equation that represents the total cost of service is: $$ y - 264.70 = 39.95(x - 6) $$
More Information
This equation shows that the total cost ( y ) includes a setup fee of $264.70 and a recurring monthly fee of $39.95 for the number of months of service.
Tips
- Confusing fixed costs (setup fee) with variable costs (monthly fee).
- Miscalculating the product of the monthly fee over the number of months.
- Forgetting to properly rearrange the equation to match the format of the choices provided.
