Answer
$510$ gallons
Work Step by Step
At the beginning of the year, the odometer read $25,124$ miles.
At the end of the year, the odometer read $37,364$ miles.
The car averaged $24$ miles per gallon.
The car traveled $ 37,364-25,124=12,240$ miles.
This means that the car used $12,240\div24=510$ gallons of gasoline.
