SOLUTION: Five years ago, a boy was 1/5 as old as his father. thirteen years from now, the boy will be half as old as his father. find the present ages of the boy and his father.

Question 1146255: Five years ago, a boy was 1/5 as old as his father. thirteen years from now, the boy will be half as old as his father. find the present ages of the boy and his father.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
b = boys present age
f = father's
:
Write an equation for each statement, simplify
:
Five years ago, a boy was 1/5 as old as his father.
b - 5 = (f-5)
multiply by 5, gets rid of the fraction
5(b-5) = f - 5
5b - 25 = f - 5
5b - 25 + 5 = f
5b - 20 = f
:
thirteen years from now, the boy will be half as old as his father.
b + 13 = (f + 13)
2(b + 13) = f + 13
2b + 26 - 13 = f
2b + 13 = f
:
find the present ages of the boy and his father.
f = f, therefore
5b - 20 = 2b + 13
5b - 2b = 13 + 20
3b = 33
b = 11 yrs is the boy's age
Find father's age using f = 2b+ 13
f = 2(11) + 13
f = 35 yrs is fathers age
:
:
Check in the statement:"Five years ago, a boy was 1/5 as old as his father."
11 - 5 = (35-5)
6 = (30)
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