A rainwater barrel was 2/3 full of water. after 60 litres of water were used from the barrel, it was 5/12 full. How much water does the barrel hold when full?
Let's represent the total capacity of the barrel with the variable "x."
We know that initially, the barrel was 2/3 full, so there must have been (2/3)x amount of water in it.
Then, 60 litres of water were used from the barrel. This means that there must have been ((2/3)x - 60) litres of water left in the barrel.
Finally, we know that after the water was used, the barrel was 5/12 full. So we can set up the equation:
((2/3)x - 60) = (5/12)x
To solve for x, we can simplify and solve for x:
(2/3)x - 60 = (5/12)x
(4/12)x - (5/12)x = 60
(-1/12)x = 60
x = -720
Since we can't have negative capacity, we made a mistake somewhere. Let's check our work:
- If the barrel was initially 2/3 full, that means there were (2/3)x litres of water in it when it was full.
- If 60 litres were used, that means there were (2/3)x - 60 litres of water left.
- If it was 5/12 full at this point, that means there must have been (5/12)x litres of water left.
So we can set up the equation:
(2/3)x - 60 = (5/12)x
Multiplying both sides by 12:
8x - 720 = 5x
3x = 720
x = 240
Therefore, the barrel can hold 240 litres of water when full.
Let's first calculate the amount of water that was initially in the barrel before any water was used.
Since the barrel was 2/3 full of water, this means that there were 2/3 of the total capacity of water in the barrel.
Let's represent the total capacity of the barrel as "x" liters.
Therefore, the initial amount of water in the barrel can be calculated as (2/3) * x.
Next, we know that after using 60 liters of water, the barrel was 5/12 full. This means that 5/12 of the total capacity of water was remaining in the barrel.
We can now create the equation:
(2/3) * x - 60 = (5/12) * x
To solve for the value of x, we can simplify the equation by multiplying both sides by 12:
12 * (2/3) * x - 12 * 60 = 5 * x
8x - 720 = 5x
Subtracting 5x from both sides:
8x - 5x = 720
3x = 720
Dividing both sides by 3:
x = 240
Therefore, the barrel can hold 240 liters of water when full.