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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