Question

Afla nr x,y,z stiind ca x + y + z= 10 si 6/x = 3/y = 11/z

Answer 1

x + y + z = 10

6/x = 3/y = 11/z = (6 + 3 + 11) / (x + y + z)
6/x = 3/y = 11/z= 20 / 10 = 2
6/x = 2  
x = 6/2 = 3
3/y = 2
y = 3/2 = 1,5
11/z = 2
 z = 11/2 = 5,5

3 + 1,5 + 5,5 = 10 

Answer 2

x + y + z = 10

6/x = 3/y = 11/z

3x = 6y ==> x = 2y
3z = 11y ==> z = 11y/3

Inlocuim in prima relatie (suma numarelor), in functie de y

2y + y + 11y/3 = 10 |×3
6y + 3y + 11y = 30
20y = 30 | :10
2y = 3
y = 3/2

x = 2 × 3/2 = 6/2 = 3

z = 11 × 3/2 × 1/3 = 33/6 = 11/2

x = 3
y = 3/2
z = 11/2

Verificam:
3 + 3/2 + 11/2 = 3 + 14/2 = 3 + 7 = 10