SOLUTION: a man has two children, a boy and a girl. the boy is 6 years older than the girl.two years ago the father's age was three times the sum of the children's ages.In eight years the fa

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Question 183149: a man has two children, a boy and a girl. the boy is 6 years older than the girl.two years ago the father's age was three times the sum of the children's ages.In eight years the father's age will be ten years greater than the sum of the children's ages.Find the present ages of the man, of the boy,and of the girl.
Answer by josmiceli(19441) (Show Source):
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Let the present age of the man =
Let the present age of the boy =
Let the present age of the girl =
2 years ago:
The man's age was
The boys aghe was
The girls age was
In 8 years:
The man's age will be
The boy's age will be
The girl's age will be
given:
(1)
(2)
(3)
-------------------------
(1)
(2)
(2)
--------------------------
(3)
(3)
--------------------------
Multiply both sides of (3) by and subtract (2) from (3)
(3)
(2)
(4)
(4)
Substitute this result back into (2)
(2)
(2)
(2)
(2)
and, from (1),
(1)
(1)
Now add (1) and (2)
(2)
(1)
(5)
(5)
Putting this back in (1),
(1)
(1)
The man is 32, the boy is 10, and the girl is 4
check answers:
(1)
(2)
(3)
--------------------------
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(3)
(3)
(3)
OK