SOLUTION: A man is three times as old as his son was at the time when the father was twice as old as the son will be in two years from now. Find the present age of each person if the sum of

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Question 186598This question is from textbook Algebra Structure and Method Book I
: A man is three times as old as his son was at the time when the father was twice as old as the son will be in two years from now. Find the present age of each person if the sum of their ages is fifty-five years. This question is from textbook Algebra Structure and Method Book I

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let f = Father's age now
Let s = Son's age now
given:
f+%2B+s+=+55
The Son's age in 2 years is
s+%2B+2
When the Father was twice as old as the Son will be in two years is
2%2A%28s+%2B+2%29
How old was the Son then?
The difference in their ages is a constant
f+-+s+=+c
s+=+f+-+c
2%2A%28s+%2B+2%29+-+c
2s+%2B+4+-+c
The Father's present age is three time the Son's at that time
f+=+3%2A2%2A%28s+%2B+2%29+-+3c
(1) f+=+6s+%2B+12+-+3c
also,
(2) f+%2B+s+=+55
(3) f+-+s+=+c
Substitute (3) in (1)
(1) f+=+6s+%2B+12+-+3%2A%28f+-+s%29
(1) f+=+6s+%2B+12+-+3f+%2B+3s
(1) 4f+-+9s+=+12
Multiply both sides of (2) by 4 and
subtract (1) from (2)
(2) 4f+%2B+4s+=+220
(1) -4f+%2B+9s+=+-12
(3) 13s+=+208
(3) s+=+16
and, since
(2) f+%2B+s+=+55
(2) f+=+55+-+16
(2) f+=+39
The father is 39 now, and the Son is 16
----------------------------------------
check answer:
The Son's age in 2 years is
16+%2B+2+=+18
When the Father was twice as old as the Son will be in two years is
2%2A%2816+%2B+2%29
36
How old was the Son then?
The difference in their ages is a constant
36+-+s+=+c
s+=+36+-+c
2%2A%28s+%2B+2%29+-+c
2s+%2B+4+-+c
The Father's present age is three time the Son's at that time
39+=+3%2A2%2A%28s+%2B+2%29+-+3c
(1) 39+=+6%2A16+%2B+12+-+3c
(1) 39+=+96+%2B+12+-+3c
(1) 3c+=+96+%2B+12+-+39
(1) 3c+=+108+-+39
(1) 3c+=+69
(1) c+=+23
and
(3) f+-+s+=+c
(3) 39+-+16+=+23
OK