Question

8 baieti si 4 fete culedg 100 kg. 18 baieti si 11 fete culeg 235 kg. Cate kg culege o fata?

Answer 1

$\left\{\begin{matrix} 8b + 4f = 100 \: \ | \times ( - 11)& \\ 18b + 11f = 235 \: | \times 4 & \end{matrix}\right.$

$\left\{\begin{matrix} - 88b - 44f = - 1100 & \\ 72b + 44f = 940& \end{matrix}\right.$

$- 88b + 72b - 44f + 44f = - 1100 + 940$

$- 16b = - 160 \: | \div ( - 16)$

$b = 10$

$8b + 4f = 100$

$8 \times 10 + 4f = 100$

$80 + 4f = 100$

$4f = 100 - 80$

$4f = 20 \: | \div 4$

$f = 5$

Answer 2

Metoda comparatiei

8 baieti ......... 4 fete ....... 100 kg     l  : 4

2 baieti .......... 1 fata ........  25 kg   l x 11

18 baieti ........ 11 fete ...... 235 kg

___________________________ egalizez nr. fete

22 baieti ........11 fete ........ 275 kg

18 baieti ......... 11 fete ........ 235 kg

_________________________ scad relatiile

4 baieti ............./..............     40 kg

40 kg : 4 = 10 kg → culege un baiat

Din relatia: 2 baieti .......... 1 fata ........  25 kg, aflam ce cantitate culege o fata

25 kg - 2 x 10 kg = 5 kg culege o fata