Margot is trying to decide between cable and satellite TV. Cable has a package of $49.99 a month for the basic package, plus $9.95 a month for a DVR and $9.95 per month for the football channel Margot wants. Margot will save $10 per month on her Internet bill if she uses the cable company for both. The Satellite TV package includes a football channel for $49.95 per month and sells a DVR for a one-time fee of $125. Over a 12-month period, which company will save Margot more money? Over a 24 month period?

The cost of cable (c) in terms of months (m) is
  c = (49.99 +9.95 +9.95 -10.00)m
  c = 59.89m

The cost of satellite TV (s) in terms of months is
  s = 125.00 +49.95m

The difference in price is ...
  s - c = (125 +49.95m) -(59.89m)
  s - c = 125 -9.94m

At 12 months, the difference in price is
  s - c = 125 -9.94*12 = 5.72
This number is positive, which means ...
  the Cable company will save Margot money over a 12-month period.

At 24 months, the difference in price is
  s - c = 125 -9.94*24 = -113.56
This number is negative, which means ...
  the Satellite TV company will save Margot money over a 24-month period.


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A graph of the costs shows a cross-over at 12.5 months. Until then, the Cable provider is less expensive. Over terms longer than that, the Satellite TV provider is less expensive.