A company is deciding between two different car models as it updates its fleet of cars. The purchase price for model A is $30,000, and the price for model B is $35,000. However, model A has an average gas mileage of 27 miles per gallon while model B’s is 36 miles per gallon. Each car in the fleet drives an average of 20,000 miles each year. If a gallon of gas costs $4, during which year of driving is the extra cost for model B made up by its superior gas mileage?
Fourth year
Fifth year
Sixth year
Seventh year
Eighth year
when is
30,000 + 4(20,000/27)t = 35000 + 4(20,000/36)t ? , where t is the number of years
30000 + 2962.96t = 35000 + 2222.22t
740.74t = 5000
t = 6.75 years
To determine during which year of driving the extra cost for model B is made up by its superior gas mileage, we can calculate the total cost of owning both car models over several years.
First, let's find the total number of gallons of gas each car would use to travel 20,000 miles:
- Model A: 20,000 miles / 27 miles per gallon = 740.74 gallons
- Model B: 20,000 miles / 36 miles per gallon = 555.56 gallons
Next, let's calculate the total cost of gas for each car model for one year of driving:
- Model A: 740.74 gallons * $4 per gallon = $2,962.96
- Model B: 555.56 gallons * $4 per gallon = $2,222.22
Now, let's find the difference in gas costs between the two models per year:
- Gas cost difference per year = Gas cost for model A - Gas cost for model B
= $2,962.96 - $2,222.22
= $740.74
To find out when the extra cost for model B is made up, we divide the price difference between the two car models by the gas cost difference per year:
- Extra cost for model B / Gas cost difference per year = ($35,000 - $30,000) / $740.74
= $5,000 / $740.74
= approximately 6.75
Since we cannot have a fraction of a year, we round up to the next whole number, which is 7.
Therefore, the extra cost for model B is made up by its superior gas mileage during the seventh year of driving.