My guess: a quarter is 25 cents right ? .....and you usually need "quarters" to use the attractions in an arcade right ?
We had penny arcades in the 60s and 70s where every attraction cost 1 penny ......did I get the joke ???! I had 3 U. S. exchange teachers in high school in Australia and they taught us many things about U.S. culture, society and psychology ......and most of my fav TV shows and rock bands were / are American and fewer were from Britain.....for us Aussues, Britain seems very far away so we turned to the U.S. for most things