SOLUTION: Five years ago, Ana was twice as old as Jamie was then. Fifteen years from now, Jamie will be as old as Ana was ten years ago. How old is Jamie now? Please solve thanks!

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Question 1151306: Five years ago, Ana was twice as old as Jamie was then. Fifteen years from now, Jamie will be as old as Ana was ten years ago. How old is Jamie now?
Please solve thanks!
Found 3 solutions by Edwin McCravy, josmiceli, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Five years ago, Ana was twice as old as Jamie was then.
A-5 = 2(J-5)
Fifteen years from now, Jamie will be as old as Ana was ten years ago.
J+15 = A-10


Simplify that system and solve it by substitution or elimination.
How old is Jamie now?
I won't tell you Jamie's age but Ana is 55.
Please solve thanks!
No, you have the equations. You solve.

Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = Jamie's age now
= Jamie's age 5 yrs ago
-------------------------------------------
= Ana's age five yrs ago
= Ana's age now
-------------------------------------------
= Jamie's age in 15 yrs




Jamie is 30 now
------------------------
check:
Five yrs ago Jamie was 25
Five yrs ago Ana was 50
------------------------------
In fifteen yrs, Jamie will be 25 + 5 + 15 = 45
Ten yrs ago, Ana was 50 - 5 = 45
This checks, Jamie is 30 now
OK

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            You can easily solve the problem using systems of two equations. 


Let A be Ana's age and J be the Jamie's age.


Then from the condition, you have this system of equations


    A - 5 = 2*(J-5)     (1)

    A - 10 = J + 15.    (2)


To solve it,  express  A = 2J - 10 + 5 = 2J - 5  from the first equation and then substitute it into the second equation.

You will get


    (2J - 10) - 5 = J + 15,

    2J - 15 = J + 15

    2J - J = 15 + 15

     J     = 30.


ANSWER.  Jamie is 30 years old;  Ana is  A = 2J-5 = 2*30-5 = 55 years old.

Solved.

----------------

There is a bunch of lessons on age word problems
    - Age problems and their solutions
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    - Really intricate age word problems
    - Selected age word problems from the archive
    - Age problems for mental solution
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Read them and become an expert in solving age problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".


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