Question 1205573
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Alex says to Sarah when I was as old as you today the sum of our ages was 27 years. 
Sarah replied when I will be as old as you are today the sum of our ages will be 55 years.
How old {{{highlight(cross(are))}}} <U>is</U> each of them.
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<pre>
Let A be the Alex's age;  S be the Sarah's age.


First sentence "Alex says to Sarah when I was as old as you today the sum of our ages was 27 years"
is translated to this equation

    [A - (A-S)] + [S - (A-S)] = 27    (it happened A-S years ago).


This equation is equivalent to

    S + 2S - A = 27,   or   3S - A = 27.    (1)


Second sentence "Sarah replied when I will be as old as you are today the sum of our ages will be 55 years"
is translated to this equation

    [S + (A-S)] + [A + (A-S)] = 55    (it will happen in A-S years).


This equation is equivalent to

    A + A + A - S = 55,   or   3A -S = 55.    (2).


So, we have the system of two equations (1) and (2).
To solve it, from equation (1) express A = 3S - 27  and substitute it into equation (2).
You will get

    3*(3S-27) - S = 55,

    9S - 81 - S = 55,

    9S - S = 55 + 81

       8S  =   136

        S  =   136/8 = 17.


Then A = 3S - 27 = 3*17 - 27 = 24.


<U>ANSWER</U>.  Alex is 24 years old;  Sarah is 17 years old.
</pre>

Solved.



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The solution by Theo is incorrect, since his setup equations are incorrect.