Let's say there are $v$ varsity players and $j$ JV players.
The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:
$\sf\implies\:(2/3)v$
And the number of JV players partnered with a varsity player is:
$\sf\implies\:(3/5)j$
Since these two numbers represent the same group of paired players, they must be equal:
$\sf\implies\:(2/3)v = (3/5)j$
To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:
$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired
$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired
So the total fraction of players who are paired is:
$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)
Simplifying:
$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$
Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.
