number puzzle

[bobobalde111]

your uncle andy sent these for you three kids said john, putting some stamps down on the table.
between three and four dozen of them
freds taken one and a half times as many as carol cried wendy its not fair.
why not im the oldest her brother declared and anyway youve taken half as many as carol and i together

how many had fred taken

[crofter]

Fred has 18 stamps, Carol has 12 and Wendy has 15

[athene]

39

[athene]

sorry, ignore that, didn't read the question properly!

[Phil7]

18

[crofter]

Solution: If there are N stamps then 36<= N <= 48
Furthermore if F, C and W denote the numbers given to each child (respectively) then F = (3/2)C and W = (F + C )/2
Written in terms of C we have W = (5/4) C.
Adding we get N = (3/2)C + (5/4)C + C = (15/4)C
Hence we have C = 4N/15 and C is integer!
We deduce that N is divisible by 15, so N must equal 45.

Therefore C = 4x45/15 = 12
It follows that F = 18 (half as much again)
and W = 15 (half of 12 plus 18)

Check: 12 + 18 + 15 = 45 (OK)