Question 319636
Let s = son's age
Let f = father's age
:
Write an equation for each statement
:
"a son is half as old as his father."
s = {{{1/2}}}f
:
"12 years ago the son was one third as old as his father."
s - 12 = {{{1/3}}}(f - 12)
multiply each side by 3, to get rid of the fraction
3(s - 12) = f - 12
3s - 36 = f - 12
3s = f - 12 + 36
3s = f + 24
Replace s with {{{1/2}}}f, (from the 1st statement)
3({{{1/2}}}f) = f + 24
({{{3/2}}}f = f + 24
Multiply both sides by 2 to get rid of the fraction, results:
3f = 2(f + 24)
3f = 2f + 48
3f - 2f = 48
f = 48 yrs is father's present age
then
{{{1/2}}}*48 = 24 yrs is son's present age

:
:
Check solutions in the statement
"12 years ago the son was one third as old as his father."
24 - 12 = {{{1/3}}}(48 - 12)
12 = {{{1/3}}}*36, confirms our solutions