A liquidity pool operated by an automated market maker contains 3000 Ether (ETH) and 9,000,000 Tether (USDT). You want to exchange 50,000 USDT into ETH. How many ETH can you take out of the pool?

Exchange rate determined by AMM. First we compute exchange ratio 9000000/3000 -> 1 ETH= 3000 USDT and this gives 27.000.000.000. When you put in 50.000 USDT that brings the total of 9050000. By scaling that back to that exchange rate you need N(ETH)*9050000= 27.000.000.000. This gives N(ETH) of 2983,43 so you can take out 3000-2983,43=16,57 ETH= 16 ETH