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2013 AMC 12B Question 10

AMC12 · 2013 AMC 12B

Question 10

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. $103$