You are trying to decide which of two automobiles to buy. The first is American-made, costs $3.0500 x 104, and travels 28.0 miles/gallon of fuel. The second is European-made, costs $4.9100 x 104, and travels 19.0 km/liter of fuel. If fuel costs $3.00/gallon, and other maintenance costs for the two vehicles are identical, how many miles must each vehicle travel in its lifetime for the total costs (puchase cost fuel cost) to be equivalent

Both cars(American and European) must travel 8,060 kilo metres each during their lifetime for the total cost(purchase cost + fuel equivalent) to be equivalent

Explanation:

With regards to the above, the cost equation for both cars will be equated together.

Furthermore, we will convert gallons into litres while also converting miles into kilometers.

Since 1 gallon has 3.785 litres; 1 mile also has 1.609 kilo metre, hence milage of the first car in kilo metre per litre would be ;

Milage American made = [ 28 miles × 1.609 ] / 3.785

= 11.90 kilo meter per litres.

Cost of Gas per litre = $3 per gallon / 3.785

= 0.79 per litre

Gas cost per kilo metre(American made) = 0.79 per litre / 11.90

= 0.066 per km

Gas cost per kilo metre(European made) = 0.79 per litre / 19.0

= 0.042 per km

We can sum up the equation of first car which is American made( Purchase price + Fuel cost)

We can make a be the number of kilo metres where total cost for both cars would be equal.

Total cost = 317.2 + 0.066a

Also, the total cost equation - purchase price + fuel cost of European car is represented as;

Total cost = 510.64 + 0.042a

317.2 + 0.066a = 510.64 + 0.042a

Collect like terms

0.066a - 0.042a = 510.64 - 317.2

0.024a = 193.44

a = 8,060 kilo metres

Therefore, both cars(American and European) must travel each 8,060 kilo metres in their life time for the total costs( purchase cost + fuel cost) to be equivalent.

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