Age Prob: Paul is 7 years older than John. If 13 is added to  TOPIC_SOLVED

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Age Prob: Paul is 7 years older than John. If 13 is added to

Postby RMEREDITH123091 on Mon Jul 06, 2009 9:32 pm

Please help me set up the equation for this problem.
Paul is 7 years older than John. If 13 is added to Paul’s age and 5 is subtracted from John’s age, Paul will be twice as old as John. How old is Paul?
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Re: Age Problem

Postby Martingale on Tue Jul 07, 2009 12:50 am

RMEREDITH123091 wrote:Please help me set up the equation for this problem.
Paul is 7 years older than John. If 13 is added to Paul’s age and 5 is subtracted from John’s age, Paul will be twice as old as John. How old is Paul?


What have you tried?
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Postby stapel_eliz on Tue Jul 07, 2009 1:46 pm

RMEREDITH123091 wrote:Please help me set up the equation for this problem.

To learn the general methodology for setting up this sort of exercise, try here. :wink:

Once you have studied the above, please attempt the exercise. If you get stuck, you can then reply with a clear listing of your steps and reasoning so far, starting with "John's age: j; Paul's age: j + 7".

Thank you! :D
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Re: Age Prob: Paul is 7 years older than John. If 13 is added to

Postby pzrose on Wed Jul 15, 2009 12:08 pm

Paul is 7 years older than John. If 13 is added to Paul’s age and 5 is subtracted from John’s age, Paul will be twice as old as John. How old is Paul?

Let x Johns age
therefore x+7 is Paul's age = x+7

add 13 to paul's age (x+7) = x+7+13
and John's age (x) = x-5
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Re: Age Prob: Paul is 7 years older than John. If 13 is added to  TOPIC_SOLVED

Postby Jesse on Wed Jul 15, 2009 8:19 pm

P=Paul's age, J=John's age

Paul is 7 years older than John.
This translates to P= 7+J

If 13 is added to Paul’s age...
This translates to P+13

...and 5 is subtracted from John’s age,...
This translates to J-5

...Paul will be twice as old as John.
This translates to P+13=2(J-5)

Now we have two equations, and can now solve for Paul's age:

(1) P=7+J
(2) P+13=2(J-5)

Solving eq.(1) in terms of P we get: J=P-7.
Substituting "P-7" for J in eq. (2), we get P+13=2(P-7-5).
Solving P+13=2(P-7-5) for P, we get P=37.
Paul is 37 year old.

To check:
First we find John's age.
John's age is found by solving 37=7+J for J. Doing so we find that John is 30 years old (J=30)

Now read the problem. Paul is 7 years older than John. He is, Paul is 37, and John is 30. If 13 is added to Paul's age (Paul will be 50) and 5 is subtracted from John's age (John will be 25), Paul will be twice as old as John (And he Is since 50 is twice as much as 25). So their ages fit the conditions of the problem!
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