Question

Sa se imparta numarul 301 in 3 parti invers proportionale cu numerele:12,10 si 18.

Answer 1

[tex]\{a,b,c\} ip \{12,10,18\} \Rightarrow \frac{a}{\frac{1}{12}}=\frac{b}{\frac{1}{10}}=\frac{c}{\frac{1}{18}}=k\Rightarrow a=\frac{k}{12},b=\frac{k}{10},c=\frac{k}{18}\\ a+b+c=301\\ \frac{k}{12}+\frac{k}{10}+\frac{k}{18}=301|\cdot 180\\ 15k+18k+10k=54180\\ 43k=54180 \Rightarrow k=1260\\ a=\frac{1260}{12}=105\\ \\ b=\frac{1260}{10}=126\\ \\ c=\frac{1260}{18}=70[/tex]