Question 678589
The systematic approach to the problem would be as follows.
STEP 1 - Define variables and understand what values they can and cannot take
{{{x}}} = John's age (That's how old John is today)
{{{y}}} = Jane's age (That's how old Jane is today)
{{{n=x-y}}} = the difference in their ages
John was, is, and will be {{{n}}} years older than Jane.
I am interpreting "was" as indicating the past,
meaning that John, who "was 2 years older than Jane is today,"
is now older than that, so he is more than 2 years older than Jane,
so {{{n>2}}}.
Jane is a teenager, so {{{12<y<20}}},
because the only numbers that end in "teen" are thirteen (13) to nineteen (19). 
 
STEP 2 - Translate phrases into algebraic expressions or equations.
John's age now is {{{x=y+n}}}, because
{{{n=x-y}}} <--> {{{x=y+n}}}
In 3 years, John will be {{{highlight(y+n+3)}}}
When John was 2 years older than Jane is today, he was {{{y+2}}}.
At that point Jane (always {{{n}}} years younger) was {{{y+2-n}}}
Four times that is {{{4(y+2-n)=highlight(4y+8-4n)}}}
In 3 years, John will be {{{highlight(y+n+3)}}},
and that number is {{{highlight(4y+8-4n)}}},
so {{{y+n+3=4y+8-4n}}}
 
STEP 3 - See what you can do with the information
We have
{{{x=y+n}}},
{{{2<n}}},
{{{12<y<20}}}, and
{{{y+n+3=4y+8-4n}}} <--> {{{y+n=4y+5-4n}}} <--> {{{n=3y+5-4n}}} <--> {{{5n=3y+5}}} <--> {{{n=(3y+5)/5}}} <--> {{{n=3y/5+1}}}
and the fact that all variables are integers.
If we want a formula to calculate {{{x}} in one step,
from {{{system(x=y+n,n=3y+5)}}} we can get {{{x=y+3y/5+1}}} --> {{x=8y/5+1}}}
 
We could try all possible values for {{{y}}},
but the only one that will make {{{n}}} and {{{x}} integers is {{{y=15}}}, so
{{{y=15}}} --> {{{x=8*15/5+1}}} --> {{{x=8*3+1}}} --> {{{highlight(x=25)}}}
So Jane is {{{15}}} and John is {{{highlight(25)}}},
The difference in their ages is, and always was {{{10}}} years.
Jane is {{{15}} today.
When John was 2 years older than {{{15}}}, John was {{{17}}}.
At that point Jane, always {{{10}}} years younger, was {{{17-10=7}}}.
In 3 years (3 years from toady), John will be {{{15+3=28}}},
and that is four times as old as {{{7}}} years old.