Question 1115373
You are looking for values for two variables,
so you need two independent equations.
 
{{{(k+n)/2=k/2+n/2}}} is half the sum of their present ages.
Jack's age was equal to that
{{{k-(k/2+n/2)=k-k/2-n/2=k/2-n/2}}} years ago.
At that point, Diane was
{{{n-(k/2-n/2)=n-k/2+n/2=3n/2-k/2=(3n-k)/2}}} .
Jack will be twice as old as that={{{3n-k}}} at some point in the future.
That is going to happen
{{{3n-k-k=3n-2k}}} years from now.
At that point Diane will be
{{{n+3n-2k=4n-2k}}} ,
and that is how old Jack is now, so
{{{k=4n-2k}}} <--> {{{3k=4n}}}
is one of the equations you need.
 
Diane's age 10 years from now will be {{{n+10}}} .
Half of that is {{{(n+10)/2=n/2+5}}} .
That was Diane's age at some point in the past.
That happened {{{n-(n/2+5)=n-n/2-5=n/2-5}}} years ago.
At that point Jack's age was
{{{k-(n/2-5)=k-n/2+5}}} ,
and that happens to be Diane"s age now, so
{{{n=k-n/2+5}}} <--> {{{3n/2=k+5}}} <--> {{{3n=2k+10}}}
is another equation you can use.
 
The system {{{system(4n=3k,3n=2k+10)}}} can be solved any way you choose.
to get {{{highlight(system(k=40,n=30))}}} .
 
{{{matrix(5,5,
" "," "," ",Jack, Diane,
10,years,ago,30,20,
5,years,ago,35,25,
" ",NOW," ",40,30,
in,10,years,50,40)}}}