Jeremy had a total of $$116$$ notes that were either $$$5$$ or $$$10$$ notes. After he spent $$60$$\% of the $$$10$$ notes and $$25$$\% of the $$$5$$ notes on a bag, he was left with~$\tfrac{4}{7}$~as many $$$10$$ notes as $$$5$$ notes. How much did the bag cost? 
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