Given the ratios of the number of games won by the teams and the number of games won by team B, we want to determine the total number of games won by all three teams, A, B, and C.
1. Calculating the Games Won by Team C:
- The ratio of games won by B to C is [tex]\(5:2\)[/tex].
- This means that for every 5 games won by team B, team C wins 2 games.
- Given that team B has won 30 games, we can set up the proportion:
[tex]\[
\frac{B}{C} = \frac{5}{2} \implies \frac{30}{C} = \frac{5}{2}
\][/tex]
- Solving for [tex]\(C\)[/tex]:
[tex]\[
C = \frac{2}{5} \times 30 = 12
\][/tex]
- Thus, team C won 12 games.
2. Calculating the Games Won by Team A:
- The ratio of games won by A to B is [tex]\(4:3\)[/tex].
- This means that for every 4 games won by team A, team B wins 3 games.
- Given that team B has won 30 games, we can set up the proportion:
[tex]\[
\frac{A}{B} = \frac{4}{3} \implies \frac{A}{30} = \frac{4}{3}
\][/tex]
- Solving for [tex]\(A\)[/tex]:
[tex]\[
A = \frac{4}{3} \times 30 = 40
\][/tex]
- Thus, team A won 40 games.
3. Calculating the Total Number of Games:
- To find the total number of games won by all three teams, we add the number of games won by each team:
[tex]\[
\text{Total games} = A + B + C = 40 + 30 + 12
\][/tex]
- Simplifying this:
[tex]\[
\text{Total games} = 82
\][/tex]
Hence, the total number of games won by the three teams combined is 82.
