PRINCE AGE RIDDLE

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Prince Age Riddle

A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess's age was half the sum of their present ages.

What are their ages?
A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess's age was half the sum of their present ages.

What are their ages?
Hint:
Current Future Past

Princess x 2z (x+y)/2
Prince y x z

I then created three equations, since the difference in their age will always be the same.

d = the difference in ages

x y = d
2z x = d
x/2 + y/2 z = d

I then created a matrix and solved it using row reduction.

x y z

1 -1 0 d
-1 0 2 d
.5 .5 -1 d

It reduced to:

x y z

1 0 0 4d
0 1 0 3d
0 0 1 5d/2

This means that you can pick any difference you want (an even one presumably because you want integer ages).

Princess age: 4d
Prince age: 3d

Ages that work

Princess:
4
8
16
24
32
40
48
56
64
72
80

Prince:
3
6
12
18
24
30
36
42
48
54
60
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