Question

A cable television provider has a $70 setup fee and charges $82 per month, while a satellite television

provider has a $175 setup fee and charges $67 per month. Let c represent the total cost in dollars and t
represent the amount of time in months.
C = 70 + 82t
The system of equations
C = 175 + 67t
can be used to represent this situation.
Part 1 out of 2
In how many months will both providers cost the same? What will that cost be?
Both providers will cost $ in months.

Answer 1

The cost of both providers will be the same after 7 months, and the cost will be $616.

Step-by-step explanation:

To find the number of months in which both providers will cost the same, we need to set up and solve the equation:

70 + 82t = 175 + 67t

First, we combine like terms:

82t - 67t = 175 - 70

15t = 105

Next, we divide both sides of the equation by 15 to solve for t:

t = 7

Therefore, both providers will cost the same after 7 months. To find the cost, we substitute the value of t into either of the original equations:

C = 70 + 82t

C = 70 + 82(7)

C = 616

So, both providers will cost $616 after 7 months.