Răspuns:
In urna A la inceput aveam 35 bile
In urna B la inceput aveam 21 bile
Explicație pas cu pas:
In urna A avem a bile , iar in urna B avem b bile
I) Luam din A cate bile sunt in B => in A raman : a-b bile
Punem in urna B b bile => b + b = 2b bile ramase in urna B
II) Luam din urna B cate bile au ramas in A adica a-b =>
2b-(a-b) = 2b-a+b = 3b-a raman in urna B
Punem in urna A a-b bile => raman in urna A 2(a-b) bile
III) Punem in ambele urne cate sunt in urna B =>
in urna A vom avea : 2(a-b) +3b-a = 2a-2b+3b-a = b+a bile
in urna B vom avea : 2(3b-a) = 6b-2a bile
A = b + a = 56 bile
B = 6b-2a = 56 bile
{ b+a = 56 I·2 => {2b + 2a = 112
{6b-2a = 56 {6b - 2a = 56
___________
8b = 168 bile => b = 21 bile
a = 56-21 = 35 bile
In urna A la inceput aveam 35 bile
In urna B la inceput aveam 21 bile
Verificare :
35-21 = 14 in A ; 21 + 21 = 42 in B
14 + 14 = 28 in A ; 42-14 = 28 in B
28+28 = 56 in A ; 28+28 = 56 in B
