Răspuns:
a) a = 88, b = 33
b) a = 80, b = 30
c) a = 88, b = 33
Explicație pas cu pas:
[tex] \frac{a}{b} = \frac{8}{3} \iff 3a = 8b\\ \\ \text{a)} a+b = 121 \\ \\ \frac{8b}{3}+b = 121\\ \\ \frac{11b}{3} = 121\\ \\ 11b = 363\\ \\ b = 33\\ \\ a = \frac{8\cdot 33}{3} = 88\\ \\ \text{b)} a-b = 50\\ \\ \frac{8b}{3}-b = 50 \\ \\ \frac{5b}{3} = 50 \\ \\ 5b = 150\\ \\ b = 30\\ \\ a = \frac{8\cdot 30}{3} = 80\\ \\ \text{c)} 3a+2b = 330\\ \\ 3\cdot\frac{8b}{3} + 2b = 330 \\ \\ 8b+2b = 330\\ \\ 10b = 330 \\ \\ b = 33\\ \\ a = \frac{8\cdot 33}{3} = 88[/tex]
