Question 1209340
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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.
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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.


<U>ANSWER</U>.  Tony is 12 years old.  Gloria is 3x = 3*12 = 36 years old.


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