Jayden and Sean were playing a card game using 128 cards. In the first game,
Sean lost 1/5
of his cards to Jayden. In the second game, Jayden lost 1/3
of his cards
to Sean. After the second game, both boys had the same number of cards.
How many cards did Jayden have at first?
after the first round
Jayden has j + 1/5 s
Sean has 4/5 s
after the second round,
Jayden has 2/3 (j + 1/5 s)
Sean has 4/5 s + 1/3 (j + 1/5 s)
so now we have
j+s = 128
2/3 (j + 1/5 s) = 4/5 s + 1/3 (j + 1/5 s)
s = 40
j = 88
check to be sure this actually works