You are trying to decide which of two automobiles to buy. The first is American-made, costs $28,500, and has a rated gasoline mileage of 28 miles/gal. The second car is of European manufacture, costs $35,700, and has a rated mileage of 19 km/L. If the cost of gasoline is $3.25/gal and if the cars actually deliver their rated mileage, estimate how many miles you would have to drive for the lower fuel consumption of the second car to compensate for the higher cost of this car.

So, the European made car must be driven at least 266666.67 kilo metres in order for both the cars to have same total cost and the European car should be driven more than 266666.67 kilo metres in order for it to have a lower total cost and provide an advantage over the american made.

Explanation:

To calculate the number of miles needed for the lower fuel consumption car to have the same cost as of the higher fuel consumption cost, we need to equate the cost equation of both the cars.

We need to convert the gallons into litres and miles into kilo metres. 1 gallon contains 3.785 litres and 1 mile contains 1.609 kilo metre. So, mileage of first car in kilo metre per Litre is,

Mileage  American made = (28 * 1.609) / 3.785

Mileage  American made = 11.90 kilo metre per litres

Gas cost per Litres = 3.25 / 3.785

Gas cost per Litres = $0.8586 rounded off to $0.86 per Litres

Gas cost per kilo metre - American Made = 0.86 / 11.90  = $0.072 per km

Gas cost per kilo metre - European Made = 0.86 / 19  = $0.045 per km

The total cost equation (purchase price + fuel cost) of first car which is American made is,

Let x be the number of kilo metres where both cars total costs are equal.

Total cost = 28500 + 0.072x

The total cost equation (purchase price + fuel cost) of first car which is European made is,

Let x be the number of kilo metres where both cars total costs are equal.

Total cost = 35700 + 0.045x

28500 + 0.072x  =  35700 + 0.045x

0.072x - 0.045x  =  35700 - 28500

0.027x  =  7200

x  =  7200 / 0.027

x  =  266666.67 kilo metres

So, the European made car must be driven at least 266666.67 kilo metres in order for both the cars to have same total cost and the European car should be driven more than 266666.67 kilo metres in order for it to have a lower total cost and provide an advantage over the american made.

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