Let \( r \) be the number of World Series won by the Cincinnati Reds. Then, the number of World Series won by the New York Yankees can be expressed as \( 5.2r \).
According to the problem, the total number of World Series won by both teams is 31. Therefore, we can set up the following equation:
\[ r + 5.2r = 31 \]
Combining the terms on the left side gives:
\[ 6.2r = 31 \]
To solve for \( r \), we divide both sides by 6.2:
\[ r = \frac{31}{6.2} \]
Calculating the right side:
\[ r = 5 \]
Now that we have the number of World Series won by the Reds, we can find the number won by the Yankees:
\[ 5.2r = 5.2 \times 5 = 26 \]
Thus, the New York Yankees won 26 World Series, and the Cincinnati Reds won 5 World Series.
In summary, the results are:
- Yankees: 26 World Series
- Reds: 5 World Series
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