SOLUTION: Tony is three times as old as Gloria. Six years ago, Tony was five times as old as Gloria. Find the present ages of Tony and Gloria.

Let Tony's age be x years;

Then Gloria 's age is 3x years, according to the problem.


Six years ago, Tony   was (x-6) years old    (1)

               Gloria was 3x-6 years ago.    (2)


We equate 5 times value of (1) and value of (2)

    5(x-6) = 3x - 6.


This is your setup equation.  Simplify and find x

    5x - 30 = 3x - 6

    5x - 3x = 30 - 6

       2x   =   24

        x   =   24/2 = 12.


ANSWER.  Tony is 12 years old.  Gloria is 3x = 3*12 = 36 years old.


CHECK.  6 years ago their ages were 6 and 30 years, with the ratio  30/6 = 5.   ! correct !