Question 573241

Looks like we'll have 2 equations here to figure out Julie and her sister's ages.  Let's use J to mean Julie's age now and S to be her sister's age now.


J = S / 2


In 7 years, Julie will be J + 7; her sister will be J + 7.  At that time, 
J will be the same age as her sister was S-5 years ago.
J+7 = S-5


Putting the two together:
J=S/2
J+7 = S-5

Substituting J from the first equation into the second equation, we get:
(S/2) + 7 = S - 5
Let's multiply both sides by 2 and get rid of that fraction thing.
S + 2(7) = 2(S) - 2(5)
S + 14 = 2S - 10
Subtract S from both sides:
14 = S - 10
Add 10 to both sides:
24 = S


Julie's sister is 24.  Since Julie is half as old as her sister, Julie is 24/2 = 12.


Let's check:
In 7 years, Julie will be 12 + 7 = 19.  She will then be the same age as her sister was 5 years ago.  Julie's sister is 24.  That means 5 years ago she was 24 - 5 = 19.  19=19.  Correct!