A rainwater was 2/3 full of water. After 60 liters of water were used from the barrel, it was 5/12 full. How much water does the barrel hold when full?

 240 liters

Work Shown:

x = capacity of barrel in liters

This value of x is some positive real number. It represents the most amount of water the barrel can hold.

The problem states that the barrel is 2/3 full to start with. This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.

We can form this equation

(2/3)x - 60 = (5/12)x

Multiply both sides by 12 to clear out the fractions

(2/3)x - 60 = (5/12)x

12*( (2/3)x - 60 ) = 12*(5/12)x

12*(2/3)x - 12*60 = 12*(5/12)x

8x - 720 = 5x

From here we solve for x

8x - 5x = 720

3x = 720

x = 720/3

x = 240

The barrel's full capacity is 240 liters

Check:

2/3 of 240 = (2/3)*240 = 160

The barrel starts off with 160 liters of water inside.

We then use 60 of them to be left with 160-60 = 100 liters

Note how 100/240 = (5*20)/(12*20) = 5/12, showing that 100 liters out of 240 total reduces to the fraction 5/12. In other words, when we say "5/12 full" we mean 100 liters full. This helps confirm we have the right answer.

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