Here's a
trip calculator you can use to figure out your toll. You will be getting on the Tollway near Cherry Valley and stay on the Tollway to the state line. In general, tolls are doubled for those without a transponder. I believe you'll only have one toll plaza to go through. I wouldn't bother trying to avoid the toll. It's probably less than 4 dollars. You'd waste time and probably spend more than that in extra fuel.
This
page explains the various ways you can get a transponder if desired. Stay to the right if you are going to pay cash.