A car uses 8.4 litres of gas for every $100 \mathrm{~km}$ it is driven. A mechanic is able to modify the car's engine at a cost of $\$ 400$ so that it will only use 6.3 litres of gas per $100 \mathrm{~km}$. The owner determines the minimum distance that she would have to drive to recover the cost of the modifications. If gas costs $\$ 0.80$ per litre, this distance, in kilometres, is between
(A) 10000 and 14000
(B) 14000 and 18000
(C) 18000 and 22000
(D) 22000 and 26000
(E) 26000 and 30000

Part C: Each correct answer is worth 8.
The cost to modify the car's engine (\$400) is the equivalent of the cost of $\frac{400}{0.80}=500$ litres of gas. So the car would have to be driven a distance that would save $500 \mathrm{~L}$ of gas in order to make up the cost of the modifications.

Originally, the car consumes $8.4 \mathrm{~L}$ of gas per $100 \mathrm{~km}$, and after the modifications the car consumes $6.3 \mathrm{~L}$ of gas per $100 \mathrm{~km}$, a savings of $2.1 \mathrm{~L}$ per $100 \mathrm{~km}$.

Thus, in order to save $500 \mathrm{~L}$ of gas, the car would have to be driven $\frac{500}{2.1} \times 100=23809.52 \mathrm{~km}$.

ANSWER: (D)