Question 1210343
<pre>
So that the problem will have only positive integer solutions, I will change the
first sentence from

<font color="indigo"><i>Matej and Anton are 44 years old together.</font></i>

to

<font color="indigo"><i>Matej and Anton are 48 years old together.</font></i>

-------------------------

<font color="indigo"><i>Matej and Anton are 48 years old together.</font></i> 

eq. 1:      M + A = 48

<font color="indigo"><i>Matej is twice as old as Anton was...</font></i>

eq. 2:      M = 2(A - ?)

Let that be x years ago.

eq. 2:      M = 2(A - x) 

<font color="indigo"><i>...when Matej was half as old as Anton will be...</font></i> 

eq. 3:      M - x = (1/2)(A + ?)

Let that be y years from now.

eq. 3       M - x = (1/2)(A + y)

<font color="indigo"><i>when Anton is 3 times older than Matej was...</font></i> 

eq. 4       A + y = 3(M - ?)

Let that be z years ago.

eq. 4       A + y = 3(M - z)

<font color="indigo"><i>when Matej was 3 times as old as Anton.</font></i>

eq. 5     M - z = 3(A - z)

<font color="indigo"><i>How old is Matej?</font></i>

{{{system(M + A = 48, M = 2(A - x),  M - x = expr(1/2)(A + y), A+y = 3(M - z), M - z = 3(A - z))}}}

One of the other tutors will probably solve it by hand. But if you go to:

https://www.wolframalpha.com/

and type in

M+A=48, M=2(A-x), M-x=(1/2)(A+y), A+y=3(M-z), M-z=3(A-z)

you will see:

A=18, M=30, x=3, y=36, z=12

So the answer is:  Matej is 30 years old.

Edwin</pre>