SOLUTION: Julie is half as old as her sister. In seven years she will be the same age as her sister was five years ago. Find the current ages of Julie and her sister.

Question 573241: Julie is half as old as her sister. In seven years she will be the same age as her sister was five years ago. Find the current ages of Julie and her sister.
Answer by mathsmiles(68) (Show Source): You can put this solution on YOUR website!

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!

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