how can you write the expression with a rationalized denominator?


3 sqrt 2 / 3 sqrt 6

see photo attached for answers

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.