Answer: approximately 95 months
Step-by-step explanation: Let’s solve this problem step by step:
The cost of the digital video recorder is $99.99 and the monthly programming service costs $12.95 per month.
Let’s say you subscribe to the programming service for “x” months. The total cost would be 99.99 + 12.95x.
The average cost per month would be (99.99 + 12.95x) / x.
We need to find the number of months “x” for which the average cost drops to $14 per month: (99.99 + 12.95x) / x = 14
Solving for “x”, we get: 99.99 + 12.95x = 14x
Subtracting 12.95x from both sides, we get: 99.99 = 1.05x
Dividing both sides by 1.05, we get: x ≈ 95.
So, you need to subscribe to the programming service for approximately 95 months before the average cost drops to $14 per month.