A tank is to be filled with water. When the tank is one-sixth full, 130 gallons of water are added, making the tank three-fifths full. How many gallons does the tank contain when it is completely full?
To solve this problem, I need to find a way to relate the fractions of the tank that are full to the amount of water that is added or removed. One way to do this is to use a variable to represent the total capacity of the tank, say C. Then, when the tank is one-sixth full, it contains C/6 gallons of water, and when it is three-fifths full, it contains 3C/5 gallons of water. The difference between these two amounts is the 130 gallons that are added, so I can write an equation: 3C/5 - C/6 = 130. To solve for C, I need to clear the fractions by multiplying both sides by the least common multiple of 5 and 6, which is 30. This gives me 18C - 5C = 3900, or 13C = 3900. Dividing both sides by 13, I get C = 300. This means that the tank has a capacity of 300 gallons, and that is the answer. 