Question

Helen and Sam had some stamps. When Helen gave away 360 stamps and
Sam gave away 48 stamps, the number of stamps Helen had was 2/5 of the
number of stamps Sam had. How many stamps did Helen have at first if she had 114 more stamps than Sam?

Answer 1

H-360 = (2/5) (S-48) = (2 S - 96) / 5
S = H - 114
------------- substitute
5 H - 1800 = 2 S - 96
5 H - 1800 = 2 (H-114) - 96
5 H - 1800 = 2 H - 228 - 96
3 H = 1476
H = 492

Answer 2

Sam had x stamps
Helen had x+114 stamps.

after the Great Give-away:
Same had x-48
Helen had x+114 - 360 = x - 246

"Helen had was 2/5 of the number of stamps Sam had"
----> x - 246 = (2/5)(x - 48)
5x - 1230 = 2x - 96
3x = 1134
x = 378

Helen originally had 378+114 or 492 stamps

check:
Sam had 378
Helen had 492

after gifting:
Sam had 378 - 48 = 330
Helen had 492 - 360 = 132
and (2/5)(330) = 132 , looking good!

Answer 3

Whew :)