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?
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 ✅