Problem Solving

There are 120 contestants vying for the Miss Idaho crown. There are 50% fewer tap dancers than 4 times the number of baton twirlers. 1/4 of the contestants are neither tap dancers nor baton twirlers. If all of the 120 contestants have only one special talent, how many are tap dancers?

Unfortunately, this wasn't a multiple choice question so I cannot post the answer, although I think I know what it is. Anyone have any ideas? Thanks in advance...

120 Contestants:

2*Tap Dancers = 1*Baton Twirlers (This is what the 50% fewer tap dancers than 4 times the number of baton twirlers means... if there were 2 times the number of baton twirlers, then it would be 0% fewer tap dancers than 2 times the number of baton twirlers. Take that one step further and you will get 100% more TD than 1 times the number of Baton Twirlers::: 2 Tap Dancers = 1 Baton Twirlers)

1/4 does neither = 30 Contestants

90 left. The ratio is 2 tap dancers to every 1 baton twirler. There are 60 tap dancers. 30 baton twirlers.

That's what i got as well...thanks so much!