Desmond and Lennon have some cards each. If Lennon gives Desmond 56 cards, they will have an equal number of cards. If Desmond gives Lennon 166 cards, the ratio of the number of cards Lennon has to the number of cards Desmond has would be 13:1. How many cards does Desmond have at first?

Answer 1

Let x be the number of cards Desmond has. Then Lennon has x+56 cards.
If Desmond gives Lennon 166 cards, Lennon will have x+56+166=(x+222) cards.
The ratio of the number of cards Lennon has to the number of cards Desmond has is (x+222):x=13:1.
Thus, (x+222)/x=13/1
x+222=13x
222=12x
x=<<18=18>>18 cards. Answer: \boxed{18}.