Notăm:
m - numărul merelor;
n - nummărul nucilor.
[tex]\it a)\ \ \dfrac{m}{n}=\dfrac{8}{5} \Rightarrow m=\dfrac{8n}{5}=8\cdot\dfrac{n}{5}\in\mathbb{N \Rightarrow } n\in M_5 \Rightarrow n\ \vdots\ 5\\ \\ \\ \ \dfrac{m}{n}=\dfrac{8}{5} \Rightarrow \dfrac{m}{8}=\dfrac{n}{5}=k,\ \ (k\in \mathbb{N}^ *),\ \Rightarrow \begin{cases} \it m=8k\\ \\ n=5k \end{cases}\ \ \ \ \ (1)[/tex]
[tex]\it m > n\ cu\ 60 \Rightarrow m=n+60 \Rightarrow m-n=60\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 8k-5k=60 \Rightarrow 3k=60|_{:3} \Rightarrow k=20\\ \\ m=8\cdot20=160\\ \\ n=5\cdot20=100[/tex]
