Question

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?

Answer 1

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.