Question

Nr a,b,c,d sunt invers proportionale cu 0,2;1/7;1/3;0,0(6),
Suma lor este 360

Answer 1

[tex]0,0(6)=\frac{6}{90}=\frac{1}{15}\\ 0,2=\frac{2}{10}=\frac{1}{5}\\ \{a,b,c,d\}i.p.\{0,2;\frac{1}{7};\frac{1}{3};0,0(6)\}=\ \textgreater \ \frac{\frac{a}{1}}{\frac{1}{5}}=\frac{\frac{b}{1}}{\frac{1}{7}}=\frac{\frac{c}{1}}{\frac{1}{3}}=\frac{\frac{d}{1}}{\frac{1}{15}}=\ \textgreater \ \\ =\ \textgreater \ \frac{a}{5}=\frac{b}{7}=\frac{c}{3}=\frac{d}{15}=k=\ \textgreater \ a=5k,b=7k,c=3k,d=15k\\ a+b+c+d=360\\ 5k+7k+3k+15k=360\\ 12k+18k=360\\ 30k=360=\ \textgreater \ k=12\\ a=5k=\ \textgreater \ a=60\\ b=7k=\ \textgreater \ b=84\\ c=3k=\ \textgreater \ c=36\\ d=15k=\ \textgreater \ d=180[/tex]