Question

Numerele a,b,c sunt direct proportionale cu numerele 2,6,7.Aflati numerele dacă :
a)a+b+c=135
b)3a+2b+5c=106

Answer 1

a)a+b+c=135
2k+6k+7k=135
15k=135
k=9
a=2k=18
b=6k=54
c=7k=63

a)3a+2b+5c=106
a=2k
b=6k
c=7k
6k+12k+35k=106
53k=106
k=2
a=2k=4
b=6k=12
c=7k=14

Answer 2

$a)~ \frac{a}{2}= \frac{b}{6}= \frac{c}{7}= \frac{a+b+c}{2+6+7}= \frac{135}{15}=9. \\ \\ \frac{a}{2}=9 \Rightarrow a=18. \\ \\ \frac{b}{6}=9 \Rightarrow b=54. \\ \\ \frac{c}{7}=9 \Rightarrow c=63.$

$b)~ \frac{a}{2}= \frac{b}{6}= \frac{c}{7}=k \Rightarrow a=2k;~b=6k;~c=7k. \\ \\ 3a+2b+5c=106 \\ 3 \cdot 2k+2 \cdot 6k+ 5 \cdot 7k=106 \\ 6k+12k+35k=106 \\ 53k=106 \Rightarrow k=2. \\ \\ a=2k = 2 \cdot 2=4. \\ b=6 k=6 \cdot 2=12. \\ c=7k=7 \cdot 2=14.$