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
