SOLUTION: A man has a daughter and a son. The son is 3 years older than the daughter. In one year the man will be six times as old as the daughter's now. In ten years the man will be 14 year

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Question 884150: A man has a daughter and a son. The son is 3 years older than the daughter. In one year the man will be six times as old as the daughter's now. In ten years the man will be 14 years old than the combined ages of his children at that time. What is the man's present age?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = the man's age now
Let +d+ = daughter's age now
Let +s+ = son's age now
----------------------------
(1) +s+=+d+%2B+3+
(2) +m+%2B+1+=+6d+
(3) +m+%2B+10+=+d+%2B+10+%2B+s+%2B+10+%2B+14+
------------------------------------
(2) +m+=+6d+-+1+
(3) +m+-+d+-+s+=+24+
Substitute (1) and (2) into (3)
(3) +6d+-+1+-+d+-+d+-+3+=+24+
(3) +4d+=+28+
(3) +d+=+7+
and
(1) +s+=+d+%2B+3+
(1) +s+=+7+%2B+3+
(1) +s+=+10+
and
(2) +m+=+6d+-+1+
(2) +m+=+6%2A7+-+1+
(2) +m+=+41+
The man is 41
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check:
The son is 3 yrs older than daughter -check
In 1 yr, man is 42, 6 times older than daughter -check
In 10 yrs, man is 51
Son and daughter will be 20 and 17
20 + 17 + 14 = 51 -check