Un numar impartit la 8 da catul c1 si restul3.Acelasi numar impartitla 10 da catul c2 si restul5,Tot
acelasi numar impartit la 12 da catul c3si restul 7.Aflati numarul daca este cuprins intre 400 si 500.
unde adunand 5 la fiecare relatie avem :
![Rendered by QuickLaTeX.com n+5=8\left ( c_{1}+1 \right ),n+5=10\left ( c_{2}+1 \right ),n+5=12\left ( c_{3}+1 \right )](https://anidescoala.ro/wp-content/ql-cache/quicklatex.com-581b30fa9a956e0aa7ed6b0bbdb7f32d_l3.png)
![Rendered by QuickLaTeX.com 400\leq 120k-5\leq 500\Rightarrow 3+\frac{45}{120}\leq k\leq 4+\frac{25}{120},k\in \mathbb{N}\Rightarrow k=4\Rightarrow n=475](https://anidescoala.ro/wp-content/ql-cache/quicklatex.com-e0d51f44fb66c7757c0fc3a30f4ad547_l3.png)
adica n+5 este multiplu de 8,10 si 12.Aflam c.m.m.c al acestor numere. [8,10,12]=120.
Atunci n+5=120k de unde rezulta n=120k-5
si cum
Multumesc