SOLUTION: Gabriella’s age is half that of her brother Sam. Four years ago, Gabriella’s age was a third that of her brother. How old was Sam two years ago

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Question 1195465: Gabriella’s age is half that of her brother Sam. Four years ago, Gabriella’s age was a third that of her brother. How old was Sam two years ago
Answer by ikleyn(52781) About Me  (Show Source):
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Gabriella’s age is half that of her brother Sam.
Four years ago, Gabriella’s age was a third that of her brother.
How old was Sam two years ago ?
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Let x be the Sam's age now.


Then Gabriela's age is x/2 years, according to the problem.


Four years ago Sam was x-4 years old;  Gabriela was x%2F2-4 years old.


The problem says that

    x%2F2-4 = %281%2F3%29%2A%28x-4%29.


It is your base equation.

To rid of the denominators, multiply both sides by 4*3 = 12.  You will get then

    6x - 48 = 4x - 16

    6x - 4x = 48 - 16

       2x   =    32

        x   =    32/2 = 16.


So, now Sam is 16 years old; Gabriela is 16/2 = 8 years old.


You may check that the condition "4 years ago" is held.


ANSWER.  Two years ago, Sam was 16-2 = 14 years old.

Solved.