Question 1188408
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5 years ago, Fred was one-third Joe’s age. 
In 10 years, he will be two-thirds of Joe’s age. 
What is Fred’s age now?
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            I read, understand and interpret the problem differently from the other tutor,

            so my solution and my answer are different.



<pre>
Let Ferd's age be F and Jow's age be J.


First equation is 

    F - 5 = {{{(1/3)*(J-5)}}}


I simplify it to

    3F - 15 = J - 5

    3F -  J = 10.      (1)



Second equation is

    F + 10 = {{{(2/3)*(J+10)}}}.


I simplify it to

    3F + 30 = 2J + 20

    3F - 2J = -10.     (2)


So, I have now this system of two equations in two unknowns

    3F -  J =  10      (1)

    3F - 2J = - 10     (2)


To solve it, apply the Eliminatiom method: from equation (1) subtract equation (2). You will get then

    -J - (-2J) = 10 - (-10)

       J       = 20.


Then from equation (1),  3F - 20 = 10,   3F = 10 + 20 = 30,  F = 30/3 = 10.


<U>ANSWER</U>.  Fred's age is 10 years;  Joe's age is 20 years.


<U>CHECK</U>.   5 years ago, they there 5 and 15 years old.
            
         In 10 years, their ages will be 20 and 30 years,

         so, the problem's conditions are satisfied.
</pre>

Solved.