I need to come up with an equation that will compare the cost of 2 air condition

Question

I need to come up with an equation that will compare the cost of 2 air conditioners. The question is whether or not a high efficiency rating will offset the cost of the ac's original price. Most importantly, I need to find out the amount of years where the two will be equal.
The first one costs $750.99 and has a kWh/year energy rating of 378. The other costs $501.99 and has an energy rating of 355 kWh/year. The charge for electricity is .1250 per kWh.

The equation should be set up where the number of years can be plugged into it and how many years it will take for them to equal out cost wise.

Please help ...

Explanation / Answer

Since you want to find the amount of years where the two will be equal, you have variable t for time.

The cost of the air conditioner is:

Initial Cost + Annual Cost (kWh/year * cost per kWh)

AC1=AC2

It seems like you may have mixed up your kWh since the more expensive one should theoretically require less energy (otherwise why would you even consider buying the more expensive one.)

750.99+355kWh/year*0.1250/kWh*t years = 501.99+378kWh/year*0.1250kWh*t years

Isolate the Variable

750.99-501.99=0.125/kWh (378-355 kWh/year) * t years

249/0.125=23t

t=1992 years

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