Answer:
Next year Aimee will be 13 years old
Explanation:
Let's call Aimee's age A, and Jamie's age J.
From the information given, we have that:
A = (1/3) * J
A + 12 = (1/2) * (J + 12)
Using the value of A from the first equation in the second one, we have:
J/3 + 12 = J/2 + 6
J/2 - J/3 = 6
J/6 = 6
J = 36
Now we can find A:
A = (1/3) * 36 = 12
So next year Aimee will be 13 years old