You typed "he" for "she" in the last part. There is no solution if
it were "he". But there is if it is "she".
John is as old as Cindy will be when John is twice as old as Cindy was when John was half as old as the sum of their current ages. Cindy is as old as John was when Cindy was half as old as she will be in ten years. How old are John and Cindy?
Let's go through it carefully, letting the number of years in the future
or in the past be represented by letters:
John is as old as Cindy will be
J = C + x (that is, x years in the future)
when John
who will be age J + x
is twice as old as Cindy was
J + x = 2(C - y) (this was y years in the past)
when John
at age J - y
was half as old as the sum of their current ages.
J - y = 1/2(J + C)
Cindy is as old as John was
C = J - z (z years in the past)
when Cindy
at age C - z
was half as old as she will be in ten years.
C - z = 1/2(C + 10)
So we have this system of equations:
J = C + x
J + x = 2(C - y)
J - y = 1/2(J + C)
C = J - z
C - z = 1/2(C + 10)
Simplifying the first:
J - C - x = 0
Simplifying the second:
J + x = 2C - 2y
J - 2C + x + 2y = 0
Simplifying the third:
J - y = 1/2(J + C)
2J - 2y = J + C
J - C - 2y = 0
Simplifying the fourth:
C = J - z
-J + C + z = 0
Simplifying the fifth:
C - z = 1/2(C + 10)
2C - 2z = C + 10
C - 2z = 10
The simplified system is:
J - C - x = 0
J - 2C + x + 2y = 0
J - C - 2y = 0
-J + C + z = 0
C - 2z = 10
Solve that and get J=40, C=30, x=10, y=5, z=10
So John is 40 and Cindy is 30.
Edwin
