# Suppose that there are two types of automobiles for purchase. Conventional: 25 mpg $35,000 pp Hybrid: 50 mpg $50,000 pp If gas costs $3 per gallon how many miles would need to be driven over...

Suppose that there are two types of automobiles for purchase. Conventional: 25 mpg $35,000 pp Hybrid: 50 mpg $50,000 pp

If gas costs $3 per gallon how many miles would need to be driven over time in order to make the Hybrid a better buy? What if $4 per gallon?

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### 1 Answer

A conventional automobile has a mileage of 25 mpg and the cost of the automobile is $35,000. On the other hand a hybrid automobile gives a mileage of 50 mpg but costs $50,000.

The difference in price between the two automobiles is 50000-35000 = 15000. If gasoline costs $3 per gallon, to make the hybrid a better buy let the minimum number of miles that the automobile has to be driven be X. When a person drives a conventional automobile X miles, the total cost incurred is (X/25)*3 + 35000. The cost incurred if a hybrid is used instead is (X/50)*3 + 50000. Equating the two gives: (X/25)*3 + 35000 = (X/50)*3 + 50000

=> (X/25 - X/50)*3 = 15000

=> X/50 = 5000

=> X = 250000 miles

If gasoline costs $4 per gallon, the cost of the two cars is equivalent after a distance X is driven where (X/25)*4 + 35000 = (X/50)*4 + 50000

=> 4*(X/50) = 15000

=> X = 187500 miles