Question

Produsul numerelor a,b si c este 480. a,b,c sunt direct proportionate cu 3,4 si 5. Aflati numerele.

Answer 1

[tex]\frac{a}{3}=\frac{b}{4}=\frac{c}{5}=k\Rightarrow\\ a=3k,b=4k,c=5k\\ abc=480\Rightarrow 3k\cdot4k\cdot5k=480\\ \Rightarrow60k^3=480\Rightarrow k^3=\frac{480}{60}=8\Rightarrow k^3=8\Rightarrow k=2\\ a=3k=6\\ b=4k=8\\ c=5k=10. [/tex]

Answer 2

$\frac{a}{3}= \frac{b}{4}= \frac{c}{5} =k \Rightarrow a=3k~;~b=4k~si~c=5k. \\ \\ abc=480 \\ \\ 3k \cdot 4k \cdot 5k=480 \\ \\ 60 k^3=480 \\ \\ k^3=8 \Rightarrow k=2. \\ \\ a=3k=3 \cdot 2 =6 \\ \\ b= 4k=4 \cdot 2=8 \\ \\ c=5k=5 \cdot 2 =10$