Let's define the number of World Series won by the Cincinnati Reds as \( r \). According to the problem, the New York Yankees won 5.2 times as many World Series as the Reds. Therefore, the number of World Series won by the Yankees can be expressed as \( 5.2r \).
The total number of World Series won by both teams is given as 31. We can set up the following equation:
\[ r + 5.2r = 31 \]
Combining the terms, we get:
\[ 6.2r = 31 \]
To find \( r \), we can divide both sides by 6.2:
\[ r = \frac{31}{6.2} = 5 \]
Now that we know the Reds won 5 World Series, we can find the number of World Series the Yankees won:
\[ 5.2r = 5.2 \times 5 = 26 \]
To summarize, the number of World Series won by each team is:
- Cincinnati Reds: 5
- New York Yankees: 26
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