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?

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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

  1. 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).
  1. 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): $$ y = S + 39.95 \times 6 $$

  1. Substitute the Known Total Cost

You know that the total cost ( y ) for setup and 6 months of service is $264.70: $$ 264.70 = S + 39.95 \times 6 $$

  1. Calculate the Monthly Costs for 6 Months

Calculate ( 39.95 \times 6 ): $$ 39.95 \times 6 = 239.70 $$

Therefore, the equation becomes: $$ 264.70 = S + 239.70 $$

  1. 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: $$ y = 25 + 39.95 \times x $$

  1. 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.
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