Question 1146255
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 = {{{1/5}}}(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 = {{{1/2}}}(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 = {{{1/5}}}(35-5)
6 = {{{1/5}}}(30)