Expert: Josh - 3/17/2011

Question
Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal?

Answer
Hi Edgar,

The unknown quantity here is the number of months it takes to achieve break even; let this be X.

The cost for the satellite system is C1 = 298.9 + 68.7*X.
The cost for the cable system is C2 = 74.8*X.

After X months, when the cost of the two systems are the same, C1 equals C2.
So, we set 298.9 + 68.7*X = 74.8*X. Then, solve for X.

Subtracting 68.7*X from both sides of the equation, we obtain
298.9 = 74.8*X-68.7*X
298.9 = 6.1*X
Dividing both sides by 6.1, we get X = 298.9/6.1 = 49 months.