We can make an equation to figure out the answer. This is a quite common equation with a flat fee and a rate above that. The equation will be the same as the line slope formula: y = mx + b.

In this case, we can say the equation is

Total = (price per gallon)(# of gallons) + flat fee

so

40.50 = .0075g + 13.50 (where g is # of gallons)

then

27 = .0075g

then

27/.0075 = g

cancel 3 from top and bottom:

9/.0025 = g

Multiply top and bottom by 4 to make the decimal easy:

36/.01

multiply top and bottom by 100:

3,600 = g

So Judy used 3,600 gallons.