Question

2. Shopping around for a freezer, John finally settled on one with a purchase price of $850. The annual

cost of operating the freezer is $40 dollar per year. When John's average cost of owning the freezer is less
than $117, he plans to shop for a new freezer. When can John shop for a new freezer? Round your answer
to the nearest month.

Answer 1

To determine when John can shop for a new freezer, we calculate his average cost of owning the freezer by adding the purchase price and annual operating cost, dividing by the number of years.

John can shop for a new freezer at the beginning of the 12th year, after the average cost drops below $117 per year.

Step-by-step explanation:

To determine when John can shop for a new freezer, we need to calculate the average cost of owning the freezer until it drops below $117. The initial purchase price of the freezer is $850, and the annual operating cost is $40.

The average cost per year (AC) can be calculated using the formula:

AC = (Initial Purchase Price + Total Operating Costs) / Number of Years

To find out in which year (n) the average cost will be less than $117, we can set up the inequality:

850 + 40n < 117n

Solving for n gives:

n > 850 / (117 - 40)

Which simplifies to:

n > 850 / 77

Calculating the exact value gives:

n > 11.03

So, John can start shopping for a new freezer after 11 full years, but since we need to round to the nearest month, we have to consider how many months into the 12th year the average cost becomes less than $117.

To calculate that, we take the decimal part .03 and multiply by 12 to get the number of months (m):

m = 0.03 '' 12

Thus:

m = 0.36 month

Since we can't have a fraction of a month, and rounding 0.36 to the nearest month is 0, John can start shopping for a new freezer right at the beginning of the 12th year.