Question
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?
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?
Answers
oobleck
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
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