One freezer costs $623.95 and uses 90 kilowatt hours (kwh) of electricity each month. A second freezer costs $500 and uses 100 kwh of electricity each month. The expected life of each freezer is 12 years. What is the minimum electric rate in cents per kwh for which the 12-year total cost (purchase price + electricity costs) will be less for the first freezer?

Let x = minimum electric rate (Cents/kWh)

Total months in 12 years is 12*12 = 144 m

1st freezer

Total cost over 12 years is

623.95 (cost) + (90 kWh/m) * (144 m) (x/100 $/kWh)

= 623.95 + 129.6x

2nd freezer

Total cost over 12 years is

500 + 100*144 * (x/100)

= 500 + 144x

For the 1st freezer to cost less over 12 years,

623.95 + 129.6x < 500 + 144x

123.95 < 14.4x

8.61 < x

Answer: The minimum rate is 8.61 cents per kWh