SOLUTION: The sum of the ages of Ruffa and Ai is 65. In 2 years Ruffa will be half as old as Ai. How old are they 3 years ago?

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Question 695564: The sum of the ages of Ruffa and Ai is 65. In 2 years Ruffa will be half as old as Ai. How old are they 3 years ago?
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
r = Ruffa's age
a = Ai's age

r + a = 65
r + 2 = 1/2 * (a + 2)

Substitute r = 65 - a into the second equation.

65 - a + 2 = 1/2 * (a + 2)
67 - a = 1/2 * (a + 2)
134 - 2a = a + 2
132 = 3a
a = 44 -----> r = 21

3 years ago:
Ai was 44 - 3 = 41 years old
Ruffa was 21 - 3 = 18 years old