You might want to check with someone at your club that will know the name of the clips on the pedals they have. That or go online to one of the bike shops and compare the pedal pics with what your gym has to get the correct name for what you need.bought some and some cleats to go with... but they were not the right cleats. Can anyone tell me about the different cleats?
My club used to have both the Look type and the SPD type, but they got rid of the Looks. I think SPD's are the most common as those are used in both mountain and road biking. Each type of cleat only mates with pedals of the same breed. There are other kinds too, but I would bet you won't encounter them at a spinning class (Times, Eggbeaters)
I hope you can take them back!!!
Irulan