A Cylinder oil tank is 1/3 full. if 3 more gallons are added the tank will half full. What is the capacity of tank?
(t / 3) + 3 = t / 2
when we add 3 it will become half so 1/2 -1/3 = 1/6
total 1/6 in cylinder is 1รท1/6=6
Hence 6 x 3 = 18
Let's assume the capacity of the cylinder oil tank is x gallons.
According to the given information, the tank is currently 1/3 full. So, the amount of oil in the tank is (1/3)x gallons.
If 3 more gallons are added, the tank will be half full. In other words, the amount of oil will be (1/2)x gallons.
We can set up the equation:
(1/3)x + 3 = (1/2)x
To solve for x, we can multiply both sides of the equation by 6 to get rid of the fractions:
6 * ((1/3)x + 3) = 6 * ((1/2)x)
2x + 18 = 3x
Next, subtract 2x from both sides:
18 = x
Therefore, the capacity of the tank is 18 gallons.
To solve this problem, we can break it down into steps:
Step 1: Identify the given information
- The cylinder oil tank is currently 1/3 (one-third) full.
- If 3 more gallons are added, the tank will be half full.
Step 2: Convert the given information into equations
- Let's say the capacity of the cylinder oil tank is 'C' gallons.
- The current volume of oil in the tank is 1/3 * C.
- If 3 more gallons are added, the new volume will be (1/3 * C) + 3 gallons.
- According to the problem, this new volume will be half the capacity of the tank, i.e., 1/2 * C.
Step 3: Set up an equation and solve for 'C'
- We can set up an equation based on the information above:
(1/3 * C) + 3 = 1/2 * C
Step 4: Solve the equation
- Multiply both sides of the equation by 6 to eliminate the denominators:
(6 * (1/3 * C) + 6 * 3) = 6 * (1/2 * C)
(2C + 18) = 3C
- Subtract 2C from both sides of the equation:
18 = C
Step 5: Calculate the capacity of the tank
- The capacity, represented by 'C', is equal to 18 gallons.
- Therefore, the capacity of the cylinder oil tank is 18 gallons.
So, the capacity of the tank is 18 gallons.