Question 1188408


let Fred’s age be {{{F}}} and Joe’s age {{{J}}}

if {{{5}}} years ago, Fred was {{{one-third }}}Joe’s age, we have


{{{F-5=J/3}}} 

{{{3F-15=J}}} .......eq.1

if in {{{10}}} years, Fred will be two-thirds of Joe’s age, we have

{{{F+10=2J/3}}} 
{{{3F+30=2J}}}
{{{3F/2+30/2=J}}}
{{{3F/2+15=J}}}.........eq.2

from eq.1 and eq.2 we have

{{{3F-15=3F/2+15}}}
{{{3F-3F/2=15+15}}}
{{{6F/2-3F/2=30}}}
{{{3F/2=30}}}
{{{3F=30*2}}}
{{{3F=60}}}
{{{F=60/3}}}
{{{highlight(F=20)}}}->answer: Fred is {{{20}}} years old now

{{{3*20-15=J}}} .......eq.1
{{{60-15=J}}} 
{{{J=45}}} ->Joe’s age now