ABC Cable, a cable TV and high speed internet provider, charges each customer $120 for installation, plus $25 per month for cable programming and high speed internet service. XYZ Cable, a competitor, charges $60 for installation and $35 per month for cable programming and high speed internet service. A customer who signs up with ABC will pay the same total amount for the service as a customer who signs up with XYZ if each pay for installation and for cable programming and internet service for how many months?
We have two different companies that each have different rates for installation and different monthly fees. We are asked to find out how many months it will take for the cost for each company to be the "same," which means we must set the two rates equal.
ABC Cable charges 120 dollars for installation plus 25 dollars a month. We do not know how many months we're working with, so we will have:
XYZ Cable charges 60 dollars for installation and 35 dollars per month. Again, we don't know how many months we're working with, but we know they will be the same, so we will have:
And, again, because we are finding the amount of months when the cost is the "same," we must set our rates equal.
120+25x = 60+35x
From here, we can solve for x, since is a single variable equation.
120 - 60 = 35x - 25x
60 = 10x
x = 6
Final answer is B, 6 months
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