Question 1148826
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Let E = 10a + b be Esher's age.

    So, the number E has the tens digit "a" and the ones digit "b".


Let M be the Marta's age.

    From the condition, we know that the Marta's age is M = 10b+a, the reversed number to the Esher's age.


We also are given that

    M + 13 = 2*(E+13),

which implies

    M = 2E + 13.


Using the decimal forms of the numbers E and M, it means that

    10b + a = 20a + 2b + 13,   or

    8b - 19a = 13.    (1)


So, from the condition, we have ONLY ONE equation for two unknown digits "a" and "b", equation (1).


But we also know that a" and "b" are INTEGER numbers between 1 and 9 each.


At this point, you can write  b = {{{(19-a)/8}}}  and  search for those integer "a" that produce integer values of "b".


It is easy to do in Excel.


In this way, I found  a= 1, b= 4.


So, the Esther age is 14 years, while Marta's age is 41 years.     <U>ANSWER</U>


You can check, on your own, that all requirements of the condition are satisfied.
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Solved.