Question

Dau coroana!determinati numerele a,b,c direct proportionale cu 0,(3);1,5;1,25 si 7a-b+3c=110

Answer 1

[tex]\{a,b,c\}dp\{0,(3);1,5;1,25\}\Rightarrow \frac{a}{\frac{1}{3}}=\frac{b}{\frac{3}{2}}=\frac{c}{\frac{5}{4}}=k\Rightarrow a=\frac{k}{3},b=\frac{3k}{2}, c=\frac{5k}{4}\\ 7a-b+3c=110\\ \frac{7k}{3}-\frac{3k}{2}+\frac{15k}{4}=110 |\cdot 12\\ 28k-18k+45k=1320\\ 55k=1320\\ k=24\\ a=\frac{k}{3}=8\\ b=\frac{3k}{2}=\frac{3\cdot 24}{2}=36\\ c=\frac{5\cdot 24}{4}=30[/tex]