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If you have a Medicare care, you can effectively ride the subway for half-price with a pay-per-ride Metrocard. And you will have to buy a Metrocard to pass through the AirTrain fare gates when you arrive at Jamaica Station.
To get the half-fare on the subway with a regular (full-price) pay-per-ride Metrocard, you must show your Medicare card to the subway booth clerk before going through the subway turnstile. The clerk will give you a paper "return ticket" which you can use for your next subway entry. And keep in mind that a pay-per-ride Metrocard purchase or refill of at least $10 yields a 7% bonus.
Although there is no senior discount on the AirTrain, if all four of you will be taking the AirTrain at both the beginning and the end of your visit, you can save a few dollars by buying one ten-trip "AirTrain only" Metrocard for $25, and using it for each member of your party.
Note that the Ely Avenue subway station on the E line is now called "Court Square/23rd Street."