+133 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...?
