13) Notăm a - numărul total al animalelor.
Notăm respectiv p, o, v, vi, c - numărul păsărilor, ovinelor, vacilor, vițeilor, cailor.
[tex]\it p=\dfrac{a}{2} \Rightarrow \dfrac{a}{2}\ r\breve{a}m\hat{a}ne \\ \\ \\ o=\dfrac{1}{3}\cdot\dfrac{a}{2} =\dfrac{a}{6} \Rightarrow \dfrac{^{3)}a}{2}-\dfrac{a}{6} =\dfrac{3a-a}{6}=\dfrac{2a}{6} =\dfrac{a}{3}\ r\breve{a}m\hat{a}ne \\ \\ \\ v=\dfrac{1}{2}\cdot\dfrac{a}{3}=\dfrac{a}{6}\Rightarrow \dfrac{a}{3} - \dfrac{a}{6} = \dfrac{a}{6} \ r\breve{a}m\hat{a}ne[/tex]
[tex]\it vi=\dfrac{2}{3}\cdot \dfrac{a}{6}=\dfrac{a}{9} \Rightarrow \dfrac{^{3)}a}{6}- \dfrac{^{2)}a}{9}= \dfrac{3a-2a}{18} = \dfrac{a}{18}\ r\breve{a} m\hat{a}ne\\ \\ \\ c=\dfrac{a}{18} = 164 \Rightarrow a = 18\cdot164 = 2952\\ \\ \\ \\ p=\dfrac{2952}{2} = 1476\ (suma\ a\ trei\ numere\ pare\ consecutive)\\ \\ \\ r-2+r+r+2 = 1476 \Rightarrow 3r=1476|_{:3} \Rightarrow r = 492[/tex]
Prin urmare, la fermă sunt:
490 de găini, 492 de rațe, 494 de gâște.
