The number of games won by five softball teams are displayed in the graph. However, the names of the teams are missing. The following clues provide information about the teams:

1. The Tigers won more games than the Eagles.

2. The Patriots won more games than the Cubs, but fewer games than the Mounties.

3. The Cubs won more than 20 games.

How many games did the Patriots win? [asy]
size(150);
defaultpen(linewidth(0.7pt)+fontsize(8));

int i = 1;

draw((0,i*5)--(60,i*5)); ++i;

fill(shift(12,0)*((4,0)--(4,10)--(8,10)--(8,0)--cycle),purple);
draw(shift(12,0)*((4,0)--(4,10)^^(8,0)--(8,10)));
draw((0,i*5)--(60,i*5)); ++i;

fill((4,0)--(4,15)--(8,15)--(8,0)--cycle,purple);
draw((4,0)--(4,15));
draw((8,0)--(8,15));

for(i = 3; i <= 4; ++i)
{
draw((0,i*5)--(60,i*5));
}

fill(shift(24,0)*((4,0)--(4,25)--(8,25)--(8,0)--cycle),purple);
draw(shift(24,0)*((4,0)--(4,25)^^(8,0)--(8,25)));
draw((0,i*5)--(60,i*5)); ++i;

fill(shift(36,0)*((4,0)--(4,30)--(8,30)--(8,0)--cycle),purple);
draw(shift(36,0)*((4,0)--(4,30)^^(8,0)--(8,30)));
draw((0,i*5)--(60,i*5)); ++i;

fill(shift(48,0)*((4,0)--(4,35)--(8,35)--(8,0)--cycle),purple);
draw(shift(48,0)*((4,0)--(4,35)^^(8,0)--(8,35)));
draw((0,i*5)--(60,i*5)); ++i;
draw((0,i*5)--(60,i*5));

xaxis(Bottom,0,60,RightTicks(" ",N=5,n=1,Size=2));
yaxis(Left,0,40,LeftTicks(Step=5,Size=2));
yaxis(Right,0,40);

label("Softball Results",(30,46));
label(rotate(90)*"Number of Wins",(-10,20));
label("Teams",(30,-10));
for(i = 0; i < 5; ++i)
{
label("?",(6+12*i,-4));
}
[/asy]
The only three teams that won more than 20 games won 25, 30, and 35 games.  Since the Patriots and the Mounties both won more games than the Cubs, the Cubs must have won 25 games.  Since the Mounties won more games than the Patriots, the Mounties won 35 games and the Patriots won $\boxed{30}$ games.