An aquarium tank is 1/6 full of water. When 2 gallons of water are added, the tank becomes 1/2 full. What is the total capacity of the aquarium tank, in gallons?
Let's start by using variables to represent the unknown quantities in the problem.
Let x be the total capacity of the aquarium tank, in gallons.
We know that the tank is initially 1/6 full of water, which means it contains (1/6)x gallons of water.
When 2 gallons of water are added, the tank becomes 1/2 full, which means it contains (1/2)x gallons of water.
Using these two pieces of information, we can set up an equation:
(1/6)x + 2 = (1/2)x
To solve for x, we can eliminate the fractions by multiplying both sides of the equation by the least common multiple of the denominators, which is 6:
6 * (1/6)x + 6 * 2 = 6 * (1/2)x
x + 12 = 3x
Subtracting x from both sides, we get:
12 = 2x
Dividing both sides by 2, we find that the total capacity of the aquarium tank is:
x = 6
Therefore, the tank has a total capacity of 6 gallons.