SOLUTION: In how many years time will Joyce be twice as old as Mensah, if Mensah is 5 years old and Joyce is thrice as old as Mensah?

This one is a good exercise to solve in your head...





























Current ages can be fully determined:

Mensah is 5yrs old --> Joyce is 3*5 = 15yrs old



So clearly, in 5yrs, when Mensah is 10yrs old, Joyce will be 20yrs old and twice Mensah's age.



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The algebraic setup, showing every step in detail: 

   Let  J = Joyce's age

   and  M = Mensah's age



(1)    J = 3*M = 3*5 = 15   (for current ages)



(2)    2(5 + x)  = 15 + x   (for future ages, unknown is "x" years for condition 2xM = J to be met)



    Multiply left side thru by 2:

    10 + 2x = 15 + x



    Subtract x from both sides:

      10 + x = 15



    Subtract 10 from both sides: 

       x = 5