An animal shelter is having a pet adoption event where owners can adopt an animal for just the cost of the vet fees. Vet fees for dogs are $15, and vet fees for cats are $13. Eight families adopt dogs and three adopt cats. The vet donates a third of the fees they were paid for the adoption checkups back to the shelter. How many dollars did the vet donate?
Please reason step by step, and put your final answer within \boxed{}.
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