Question

Imparti numarul 4625 in parti invers proportionale cu 8, 12, si 10

Answer 1

[tex]\{a,b,c\} ip \{8,12,10\} \Rightarrow \frac{a}{\frac{1}{8}}=\frac{b}{\frac{1}{12}}=\frac{c}{\frac{1}{10}}=k\Rightarrow a=\frac{k}{8}.b=\frac{k}{12},c=\frac{k}{10}\\ a+b+c=4625\\ \frac{k}{8}+\frac{k}{12}+\frac{k}{10}=4625|\cdot 120\\ 15k+10k+12k=555000\\ 37k=555000\Rightarrow \boxed{\boxed{k=15000}}\\ a=\frac{15000}{8}=1875\\ \\ b=\frac{15000}{12}=1250\\ \\ c=\frac{15000}{10}=1500[/tex]