SOLUTION: Samantha is 6 years older than her brother. Four years ago she was 3 times his age, and last year she was twice his age. How old are Samantha and her brother?
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Question 1061437: Samantha is 6 years older than her brother. Four years ago she was 3 times his age, and last year she was twice his age. How old are Samantha and her brother? Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website! Hi there,
Samantha is 6 years older than her brother.
S = 6 + B........Eq(1)
Four years ago she was 3 times his age,
S - 4 = 3(B - 4).......Eq(2)
Last year she was twice his age.
S - 1 = 2(B - 1).......Eq(3)
...............
Substitute (6 + B) for S in Eq(2)
S - 4 = 3(B - 4).......Eq(2)
(6 + B) - 4 = 3(B - 4)
6 + B - 4 = 3B - 12
Collect like terms
B - 3B = -14
-2B = -14
B = 7
Substitute (6 + B) for S in Eq(3)
S - 1 = 2(B - 1).......Eq(3)
(6 + B) - 1 = 2(B - 1)
6 + B - 1 = 2B - 2
Collect like terms
B - 2B = -2 - 5
-B = -7
B = 7
Brother is 7 years old
Sister is 13 years old.
Hope this helps :-)
