A si B consuma pasunea in 45 de zile
⇒ A si B consuma zilnic 1/45 din pasune
⇒ Ecuatia: A + B = 1/45
A si C consuma pasunea in 60 de zile
⇒ A si C consuma zilnic 1/60 din pasune
⇒ Ecuatia: A + C = 1/60
B si C consuma pasunea in 90 de zile
⇒ B si C consuma zilnic 1/90 din pasune
⇒ Ecuatia: B + C = 1/90
Scriem sistemul de ecuatii:
[tex]\displaystyle\\
A + B = \frac{1}{45}\\\\
A + C = \frac{1}{60}\\\\
B + C = \frac{1}{90}\\
-------- ~~~\text{Adunam ecuatiile.}\\\\
A+B+A+C+B+C = \frac{1}{45}+\frac{1}{60}+\frac{1}{90}\\\\
2A+2B+2C = \frac{1}{45}+\frac{1}{60}+\frac{1}{90}\\\\
\text{Calculam cmmmc al numerelor 60 si 90}\\
\text{fara 45 deoarece 45 este divizor al lui 90.}\\
60 = 2 \times 30\\
90 = 3\times 30\\
\text{cmmm } = 2\times3\times30 = \boxed{180}
[/tex]
[tex]\displaystyle\\
2A+2B+2C = \frac{1}{45}+\frac{1}{60}+\frac{1}{90}\\\\
2(A+B+C) = \frac{4\times 1}{4\times45}+\frac{3\times1}{3\times60}+ \frac{2\times1}{2\times90}\\\\
2(A+B+C) = \frac{4}{180}+\frac{3}{180}+ \frac{2}{180}\\\\
2(A+B+C) = \frac{4+3+2}{180}\\\\
2(A+B+C) = \frac{9}{180}\\\\
2(A+B+C) = \frac{1}{20}~~~\Big|:2\\\\
A+B+C=\frac{1}{2\times20}\\\\
A+B+C=\frac{1}{40}
[/tex]
⇒ A, B si C consuma zilnic 1/40 din pasune.
⇒ A, B si C consuma pasunea in 40 de zile
