#1**0 **

*Joe, Alex and Sean shared some stamps in the ratio 3:8:5. Sean kept *

*1/5 of his stamps for himself and gave the rest of his stamps to Joe and*

*Alex in the ratio 3:5. As a result, Alex had 96 stamps more than Joe.*

*How many stamps did Joe have in the end?*

Let's say they all have x stamps.

Joe has x * 3/16 stamps, Alex with x * 1/2, and Sean with x * 5/16.

After giving away his stamps, Sean has 1/16 * x stamps.

Joe got (1/4 * x) * 3/8 = 3/32 * x stamps. Joe now has (3/32 + 3/16)x = *9/32 x stamps.*

Alex got (1/4 * x) * 5/8 = 5/32 * x stamps. Alex now has (5/32 + 1/2)x = *21/32 x stamps*

21/32 x = 9/32 x + 96

12/32 x = 3/8 x = 96

x = 256.

256 * 9/32 = **72.**

The guests apparently gave you correct answers. Is there a mistake/misinterpretation anywhere?

(in case of a mistake, let's check)

256 stamps means Joe has 48 stamps, Alex has 128 stamps, and Sean has 80 stamps.

Sean now has 16 stamps, and 64 stamps were given away in the ratio 3/5.

24 stamps given to Joe, 40 stamps given to Alex.

Joe has 72 stamps, Alex has 168.

72+168+16 = 256

168-72 = 96

I don't see a problem...?

tinfoilhat Dec 22, 2021