Challenge:

When a can of soup is half full, it weighs 5 kg. When it is 1 third full, it ways 4 kg. What is the weight of the full can?

The trick here is that both times, part of the weight is soup

and part of the weight is the empty metal can.

1/2 soup + MTcan = 5

1/3 soup + MTcan = 4

Before going any further, it will make it a lot easier later if we change

the fractions in both equations to a common denominator:

1/2 = 3/6

1/3 = 2/6

3/6 soup + 1 MTcan = 5

2/6 soup + 1 MTcan = 4

Subtract the 2nd equation from the 1st one:

1/6 soup = 1

Multiply each side by 6 : 1 soup = 6

Substitute this in the first equation:

1/2 soup + 1 MTcan = 5

1/2 (6) + 1 MTcan = 5

3 + 1 MTcan = 5

Subtract 3 from each side: 1 MTcan = 2

The empty can weighs 2.

All the soup it can hold weighs 6.

A full can of soup weighs (2 + 6) = 8