Question 1068792
{{{x}}}= John's age (in years)
{{{y}}}= Jack's age (in years),
and we assume no tricks, as if both had birthdays on the same day.
Jack uses the phrase "when I was your age," implying that {{{y>x}}} ,
but we know that the difference in ages is {{{y-x}}} years.
So, {{{y-x}}} years ago, Jack was Jon's age, and
John was {{{y-x}}} years younger than he is now, so his age was
{{{x-(y-x)=x-y+x=2x-y}}} .
Jack says he is twice as old as that, so
{{{y=2(2x-y)}}}<--->{{{y=4x-2y}}}<--->{{{highlight(3y=4x)}}} .
Jack says "when you are my age, our ages together will be 63."
That is in the future, {{{y-x}}} years into the future,
since that is the difference in their ages.
At that point,
John's age will be {{{y}}} (Jack's current age), and
Jack's age will be
{{{y+(y-x)=2y-x}}} .
The sum of their ages at that point will be
{{{y+(2y-x)=63}}} <--->{{{highlight(3y-x=63)}}} .
We have a system of 2 linear equations with 2 variables to solve.
There are many ways to go from initial set of equations to solutions.
Here is the scenic zig-zaggy way:
{{{system(3y=4x,3y-x=63)}}}-->{{{system(3y=4x,4x-x=63)}}}-->{{{system(3y=4x,3x=63)}}}-->{{{system(y=4x/3,3x=63)}}}-->{{{system(y=4x/3,x=63/3)}}}-->{{{system(y=4x/3,x=21)}}}-->{{{system(y=4*21/3,x=21)}}}-->{{{highlight(system(y=28,x=21))}}}