document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "i am going around in circles with this! please help?? \n" ); document.write( "
Algebra.Com's Answer #421582 by KMST(5328)\"\" \"About 
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The systematic approach to the problem would be as follows.
\n" ); document.write( "STEP 1 - Define variables and understand what values they can and cannot take
\n" ); document.write( "\"x\" = John's age (That's how old John is today)
\n" ); document.write( "\"y\" = Jane's age (That's how old Jane is today)
\n" ); document.write( "\"n=x-y\" = the difference in their ages
\n" ); document.write( "John was, is, and will be \"n\" years older than Jane.
\n" ); document.write( "I am interpreting \"was\" as indicating the past,
\n" ); document.write( "meaning that John, who \"was 2 years older than Jane is today,\"
\n" ); document.write( "is now older than that, so he is more than 2 years older than Jane,
\n" ); document.write( "so \"n%3E2\".
\n" ); document.write( "Jane is a teenager, so \"12%3Cy%3C20\",
\n" ); document.write( "because the only numbers that end in \"teen\" are thirteen (13) to nineteen (19).
\n" ); document.write( "
\n" ); document.write( "STEP 2 - Translate phrases into algebraic expressions or equations.
\n" ); document.write( "John's age now is \"x=y%2Bn\", because
\n" ); document.write( "\"n=x-y\" <--> \"x=y%2Bn\"
\n" ); document.write( "In 3 years, John will be \"highlight%28y%2Bn%2B3%29\"
\n" ); document.write( "When John was 2 years older than Jane is today, he was \"y%2B2\".
\n" ); document.write( "At that point Jane (always \"n\" years younger) was \"y%2B2-n\"
\n" ); document.write( "Four times that is \"4%28y%2B2-n%29=highlight%284y%2B8-4n%29\"
\n" ); document.write( "In 3 years, John will be \"highlight%28y%2Bn%2B3%29\",
\n" ); document.write( "and that number is \"highlight%284y%2B8-4n%29\",
\n" ); document.write( "so \"y%2Bn%2B3=4y%2B8-4n\"
\n" ); document.write( "
\n" ); document.write( "STEP 3 - See what you can do with the information
\n" ); document.write( "We have
\n" ); document.write( "\"x=y%2Bn\",
\n" ); document.write( "\"2%3Cn\",
\n" ); document.write( "\"12%3Cy%3C20\", and
\n" ); document.write( "\"y%2Bn%2B3=4y%2B8-4n\" <--> \"y%2Bn=4y%2B5-4n\" <--> \"n=3y%2B5-4n\" <--> \"5n=3y%2B5\" <--> \"n=%283y%2B5%29%2F5\" <--> \"n=3y%2F5%2B1\"
\n" ); document.write( "and the fact that all variables are integers.
\n" ); document.write( "If we want a formula to calculate \"x%7D%7D+in+one+step%2C%0D%0Afrom+%7B%7B%7Bsystem%28x=y%2Bn%2Cn=3y%2B5%29\" we can get \"x=y%2B3y%2F5%2B1\" --> {{x=8y/5+1}}}
\n" ); document.write( "
\n" ); document.write( "We could try all possible values for \"y\",
\n" ); document.write( "but the only one that will make \"n\" and \"x%7D%7D+integers+is+%7B%7B%7By=15\", so
\n" ); document.write( "\"y=15\" --> \"x=8%2A15%2F5%2B1\" --> \"x=8%2A3%2B1\" --> \"highlight%28x=25%29\"
\n" ); document.write( "So Jane is \"15\" and John is \"highlight%2825%29\",
\n" ); document.write( "The difference in their ages is, and always was \"10\" years.
\n" ); document.write( "Jane is \"15%7D%7D+today.%0D%0AWhen+John+was+2+years+older+than+%7B%7B%7B15\", John was \"17\".
\n" ); document.write( "At that point Jane, always \"10\" years younger, was \"17-10=7\".
\n" ); document.write( "In 3 years (3 years from toady), John will be \"15%2B3=28\",
\n" ); document.write( "and that is four times as old as \"7\" years old. \n" ); document.write( "
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