Weekly Challenge 50: How Old?

Thanks to Thomas Udale from Winchester College for this solution, which was the age of me and my two children at the time of writing the problem :-)

Joseph's age = x
Jasmine's age = y
your age = z

from sentence 1 :   x+1=2(y+1)
from sentence 2:    66 = x+y+2n = z+n
from sentence 3:    z+6=m(x+y+12)

z < 66
z+6 < 72
m(x+y+12) < 72
m(x+y+12) = m(3y+13)

m must be a positive integer, because it is the multiple, greater than 1

if m = 4, then m(3y+13) > 72

if m = 2:
then z+6 = 6y+26
from equation 1 into equation 2 : z + n = 3y +1 +2n
z = 6y+ 20 = 3y + 1 + n
n = 3y + 19
equation 2:
3y + 2(3y+12) +1 = 66
  y = 3,
  x = 7,
  z = 38,

if m = 3,
following same as above,
n = 6y + 38
3y + 2(6y+38) + 1 = 66
15y + 77 = 66,
so y would be negative.