Ian had 140 more stickers than Ethan. Ian gave 25% of his stickers to Ethan. Ethan in return gave 80% of his stickers to Ian. In the end, Ian had 282 more stickers than Ethan. How many stickers did Ian have at first?

Answer 1

If Ethan started out with x, then Ian had x+140. So
after 1st gift:
Ian had 3/4 (x+140) = 3/4 x + 105
Ethan had x + 1/4 (x+140) = 5/4 x + 35
after the second gift we have
(3/4 x + 105) + 4/5 (5/4 x + 35) = 282 + 1/5 (5/4 x + 35)
x = 104
so Ian started out with 244
check:
Ian gave 61, retaining 183, and Ethan had 104+61 = 165
Ethan gave 132, retaining 33, and Ian had 315 = 33+282 ✅