Question 105932
Start by letting R = Robert's present age and F = Father's present age.
From the problem you can write:
1) {{{R = (1/2)F}}} "Robert (R) is half as old as his father (F)"
2) {{{R-12 = (1/3)(F-12)}}} "Twelve years ago, he was 1/3 as old as his father was then"
So now you have a system of equations with two unknowns (R and F) and you can use any of the accepted methods for solving these for R and F.
You can simplify these equations by clearing the fractions.
1) {{{R = (1/2)F}}} Multiply through by 2.
1a) {{{2R = F}}}
2) {{{R-12 = (1/3)(F-12)}}} Multiply through by 3.
2a) {{{3R-36 = F-12}}} Now substitute the F from the simplified equation 1a) into the simplified equation 2a).
{{{3R-36 = 2R-12}}} Simplify and solve for R by subtracting 2R from both sides.
{{{R-36 = -12}}} Add 36 to both sides.
{{{R = 24}}} This is Robert's present age.
{{{F = 2R}}}
{{{F = 2(24)}}}
{{{F = 48}}} This is the father's present age.
Check:
{{{R = (1/2)F}}}
{{{24 = (1/2)(48)}}}
{{{24 = 24}}} OK, and...
{{{R-12 = (1/3)(F-12)}}}
{{{24-12 = (1/3)(48-12)}}}
{{{12 = (1/3)(36)}}}
{{{12 = 12}}} OK