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
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)