$4$ cupcakes cost $16\div2=8$ dollars, so one cupcake cost $8\div4=2$ dollars. 
Kate bought $$2$$ apple pies and Lucy bought $$4$$ cupcakes. They each paid the same amount of money and together they paid $$16$$ dollars. How many dollars does $$1$$ cupcake cost? 
Options:
a: $$2$$ 
b: $$4$$ 
c: $$6$$ 
d: $$10$$ 
e: $$12$$ 