How old?
How old are these three people?
Age
14 to 18
Challenge level
Problem
Joseph recently noticed that this time next year he will be twice as old as Jasmine.
I couldn't help noticing that when I am 66 at this time of year the combined future ages of Joseph and Jasmine will also be 66.
Also, 6 years from now my future age will be a multiple of the sum of Joseph and Jasmine's future ages. Of course, all ages are non-negative integers.
How old are Joseph, Jasmine and I now?
I couldn't help noticing that when I am 66 at this time of year the combined future ages of Joseph and Jasmine will also be 66.
Also, 6 years from now my future age will be a multiple of the sum of Joseph and Jasmine's future ages. Of course, all ages are non-negative integers.
How old are Joseph, Jasmine and I now?
Getting Started
Student Solutions
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.
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.