SOLUTION: C's age is 6 more than the sum of the ages of A and B. Five years from now A will be half as old as C is now. Five years ago A was 1/3 as old as B will be five years hence. Find th

Question 1169522: C's age is 6 more than the sum of the ages of A and B. Five years from now A will be half as old as C is now. Five years ago A was 1/3 as old as B will be five years hence. Find their present ages.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement, try to get b and c in term of a
:
C's age is 6 more than the sum of the ages of A and B.
c = a + b + 6
Five years from now A will be half as old as C is now.
a + 5 = .5c
multiply both sides by 2
2(a+5) = c
c = 2a + 10
Five years ago A was 1/3 as old as B will be five years hence.
a - 5 = (b+5)
Get rid of the annoying fraction, multiply both sides by 3
3(a-5) = b + 5
3a - 15 = b + 5
3a - 15 - 5 = b
b = 3a - 20
in the first equation replace c with (2a+10), replace b with (3a-20)
2a + 10 = a + (3a - 20) + 6
2a + 10 = 4a - 14
10 + 14 = 4a - 2a
24 = 2a
a = 12 yrs
then
b = 3(12) - 20
b = 16 yrs
and
c = 2(12) + 10
c = 34 yrs
:
See if that checks out in the first equation
34 = 12 + 16 + 6
34 = 34

Find their present ages.
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