SOLUTION: Marie is 9 years older than her brother Richard. Six years ago Richard was 1/2 as old as Marie. How old are they now?

Question 1004198: Marie is 9 years older than her brother Richard. Six years ago Richard was 1/2 as old as Marie. How old are they now?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call their ages NOW, m and r.
From the facts we have
m = r + 9
r - 6 = (1/2)(m - 6)
We can substitute the first equation into the second and simplify...we get
r - 6 = (1/2)(r + 9 - 6)
r - 6 = (1/2)(r + 3)
r - 6 = (1/2)r + 3/2
Collecting like terms
(1/2)r = 6 + 3/2 = 15/2
r = 15
which means that
m = 24
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