Let's use a system of equations to solve this problem. Let B represent the number of liters a bucket can hold, and let C represent the number of liters a barrel can hold.
From the given information, we have two equations:
1. C = B + 35 (A barrel holds 35 liters more than a bucket.)
2. 3B + C = 103 (3 buckets and 1 barrel hold 103 liters.)
Now, we can substitute the value of C from the first equation into the second equation:
3B + (B + 35) = 103
Now, we can simplify the equation:
4B + 35 = 103
Subtract 35 from both sides:
4B = 103 - 35
4B = 68
Now, divide both sides by 4 to solve for B (the number of liters a bucket can hold):
B = 68 / 4
B = 17
Now that we know the number of liters a bucket can hold (B = 17), we can find the number of liters a barrel can hold using the first equation:
C = B + 35
C = 17 + 35
C = 52
So, a barrel can hold 52 liters.