SOLUTION: Matej and Anton are 44 years old together. Matej is twice as old as Anton was when Matej was half as old as Anton will be when Anton is 3 times older than Matej was when Matej was

Question 1210343: Matej and Anton are 44 years old together. Matej is twice as old as Anton was when Matej was half as old as Anton will be when Anton is 3 times older than Matej was when Matej was 3 times as old as Anton.
How old is Matej?

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

So that the problem will have only positive integer solutions, I will change the
first sentence from

Matej and Anton are 44 years old together.

to

Matej and Anton are 48 years old together.

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

Matej and Anton are 48 years old together. 

eq. 1:      M + A = 48

Matej is twice as old as Anton was...

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

Let that be x years ago.

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

...when Matej was half as old as Anton will be... 

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

Let that be y years from now.

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

when Anton is 3 times older than Matej was... 

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

Let that be z years ago.

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

when Matej was 3 times as old as Anton.

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

How old is Matej?



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

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