Question 1170837
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Let x be the age of Monica an
    y be the age of Mario.


The first statement "In eight years, Monica will be 4/5 the age of her brother Mario", means, by DEFAULT 

    "In eight years, Monica will be 4/5 the age of her brother Mario at that time".


The precise mathematical translation is THIS exaction

    x + 8 = {{{(4/5)*(y+8)}}}.


Simplify this equation

    5x + 40 = 4(y + 8)

    5x + 40 = 4y + 32

    5x - 4y = -8          (1)



The second statement "Four years ago, Monica was half as old as her brother", means, by DEFAULT, 

    "Four years ago, Monica was half as old as her brother at that time".


The precise mathematical translation is THIS exaction

    x - 4 = {{{(1/2)*(y-4)}}}.


Simplify this equation

    2x - 8 = y - 4

    2x - y = 8 - 4

    2x - y = 4            (2)



To solve the system of two equations (1) and (2), express y = 2x - 4 from (2) and substitute it into (1).  You will get then

    5x - 4*(2x-4) = -8,    or


    5x - 8x + 16  = -8

    -3x           = -8 - 16 = -24,

      x                     = 8.


Then from equation (2),  y = 2*8 - 4 = 16 - 4 = 12.


<U>ANSWER</U>.  Mario is 12 years old.
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Solved.