Question

Challenge:

Answer 1

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