Question

Esther has five times as many cards as Richard. Esther gave 1/4 of her cards to Richard. Then, Richard gave 1/6 of his cards to Esther in return. In the end, Esther has 90 cards more than Richard. How many cards did Esther have at first.

Answer 1

e = 5r
e - e/4 + 1/6 (r + e/4) = 90 + 5/6 (r+e/4)

5r - 5r/4 + 1/6 (r + 5r/4) = 90 + 5/6 (r+5r/4)
r=40
so, e=200

check:
Esther has 200, Richard has 40
Esther gives Richard 50 cards. Now they have
Esther: 150, Richard: 90
Richard gives Esther 15, so they now have
Esther: 165, Richard 75

165 = 75+90

Answer 2

Thank you Steve