Let's assume Kevin's gas tank can hold "x" gallons of gas.
Given:
1. Initially, the gas tank is 1/6 full.
2. After buying 11 gallons, it's 2/3 full.
So, we can set up the equation:
Initial amount + 11 gallons = 2/3 of the tank's capacity
(1/6)x + 11 = (2/3)x
Now, let's solve for x:
First, subtract (1/6)x from both sides:
11 = (2/3)x - (1/6)x
To add the fractions on the right side, we need a common denominator, which is 6:
11 = (4/6)x - (1/6)x
Now, combine the fractions:
11 = (3/6)x
Now, multiply both sides by 6/3 to solve for x:
11 = (6/3)x
(6/3)x = 11
x = (3/6) * 11
x = 33/6
x = 5.5
So, Kevin's gas tank can hold 5.5 gallons of gas.