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2013 AMC 10B Question 17

AMC10 · 2013 AMC 10B

Question 17

Alex has $75$ red tokens and $75$ blue tokens. There is a booth where Alex can give two red tokens and receive in return a silver token and a blue token, and another booth where Alex can give three blue tokens and receive in return a silver token and a red token. Alex continues to exchange tokens until no more exchanges are possible. How many silver tokens will Alex have at the end?
  1. $ 62 $
  2. $ 82 $
  3. $ 83 $
  4. $ 102 $
  5. $ 103 $