SOLUTION: John and jane have their birthday today. in 3 yrs, john will be four times as old as jane was when john was 2 years older than jane is today. Find john's age if jane is a teenager?

Question 678589: John and jane have their birthday today. in 3 yrs, john will be four times as old as jane was when john was 2 years older than jane is today. Find john's age if jane is a teenager?
i am going around in circles with this! please help??
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The systematic approach to the problem would be as follows.
STEP 1 - Define variables and understand what values they can and cannot take
= John's age (That's how old John is today)
= Jane's age (That's how old Jane is today)
= the difference in their ages
John was, is, and will be 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 .
Jane is a teenager, so ,
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 , because
<-->
In 3 years, John will be
When John was 2 years older than Jane is today, he was .
At that point Jane (always years younger) was
Four times that is
In 3 years, John will be ,
and that number is ,
so

STEP 3 - See what you can do with the information
We have
,
,
, and
<--> <--> <--> <--> <-->
and the fact that all variables are integers.
If we want a formula to calculate we can get --> {{x=8y/5+1}}}

We could try all possible values for ,
but the only one that will make and , so
--> --> -->
So Jane is and John is ,
The difference in their ages is, and always was years.
Jane is , John was .
At that point Jane, always years younger, was .
In 3 years (3 years from toady), John will be ,
and that is four times as old as years old.
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