Let's assign variables to represent the number of games won by each team:
Let x be the number of games won by Team A.
Let y be the number of games won by Team B.
Let z be the number of games won by Team C.
From the given information, we can form the following equations:
Equation 1: x + y + z = 60 (The total number of games won by the three teams is 60.)
Equation 2: x = (1/2)y (Team A won 50% as many games as Team B.)
Equation 3: x + y = 1.5z (Team A and Team B together won 50% more games than Team C.)
Now, let's solve this system of equations:
Substituting Equation 2 into Equation 3, we get:
(1/2)y + y = 1.5z
(3/2)y = 1.5z
y = (1.5z) * (2/3)
y = z
Substituting y = z into Equation 1, we have:
x + y + z = 60
x + y + y = 60
x + 2y = 60
Substituting y = z into Equation 3, we have:
x + y = 1.5z
x + y = 1.5y
x = 0.5y
Now, we can substitute x = 0.5y and y = z into Equation 1:
0.5y + 2y = 60
2.5y = 60
y = 60 / 2.5
y = 24
Substituting y = 24 into x = 0.5y:
x = 0.5 * 24
x = 12
Substituting y = 24 into the equation y = z:
z = 24
Therefore, Team A won 12 games, Team B won 24 games, and Team C won 24 games as well.