Mary and Andy had a total of 200 game cards. Mary gave Andy 1/2
of her cards.
Then, Andy gave 2/7
of all his cards to Mary. They both ended with the same
number of cards. How many cards did Andy have at first?
m + a = 200
mary: ....... andy
m-.5m ,...., a + .5 m
m-.5 m + 2/7(a+.5m) ,...., 5/7(a + .5 m )
(.5+1/7)m + 2/7 a = 5/7 a + 5/14 m
9/14 m + 4/14 a = 10/14 a + 5/14 m
4 m = 6 a
m = 3/2 a
so
3/2 a + 2/2 a = 400/2
5 a = 400
a = 80