SOLUTION: 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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Question 1188408: 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?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let Fred’s age be and Joe’s age
if years ago, Fred was Joe’s age, we have


.......eq.1
if in years, Fred will be two-thirds of Joe’s age, we have



.........eq.2
from eq.1 and eq.2 we have







->answer: Fred is years old now
.......eq.1

->Joe’s age now

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~


            I read, understand and interpret the problem differently from the other tutor,
            so my solution and my answer are different. 


Let Ferd's age be F and Jow's age be J.


First equation is 

    F - 5 = 


I simplify it to

    3F - 15 = J - 5

    3F -  J = 10.      (1)



Second equation is

    F + 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.


ANSWER.  Fred's age is 10 years;  Joe's age is 20 years.


CHECK.   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.

Solved.



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