Explanation:
x = max number of gallons the tank can hold
Greg's car starts off 1/3 full, so (1/3)x = x/3 number gallons is in the car.
Add on 11 more gallons to get (x/3) + 11 = x/3+33/3 = (x+33)/3
The expression (x+33)/3 represents the number of gallons he has after buying 11 gallons of gas. This is equal to (5/6)x since this represents the idea of the tank being 5/6 full
The equation we need to solve is (x+33)/3 = (5/6)x
Let's do so to get...
(x+33)/3 = (5/6)x
(x+33)/3 = (5x)/6
6(x+33) = 3*5x
6x+198 = 15x
198 = 15x-6x
198 = 9x
9x = 198
x = 198/9
x = 22
His tank can hold up to 22 gallons.
