Question

Trei elevi au rezolvat 24 ; 27  si respectiv 30 de probleme. Stiind ca au primit note direct proportionale cu numarul de exercitii rezolvate si ca media notelor este 9 , sa se afle ce nota a obtinut fiecare. CE procent reprezinta nota primului elev din cea obtinuta de al treilea elev ? 
Va rog... ma poate ajuta cineva? 

Answer 1

$24;27;30 \ \ \ \ d.p \\ x;y;z \\\\\\ \frac{24}{x}=\frac{27}{y}= \frac{30}{z}=k \\\\ x= \frac{24}{k} \\\\ y= \frac{27}{k} \\\\ z=\frac{30}{k} \\\\m_a=9 \\\\ m_a\frac{\frac{24}{k}+\frac{27}{k}+\frac{30}{k}}{3} \\\\ m_a=\frac{81}{k}*\frac{1}{3} \\\\ m_a= \frac{27}{k} \\\\ \frac{27}{k}=9 \\\\ k= \frac{27}{9} \\\\ \boxed{k=3} \\\\ x=\frac{24}{3}\to\boxed{\boxed{8}} \\\\ y= \frac{27}{3}\to\boxed{\boxed{9}} \\\\ z=\frac{30}{3}\to \boxed{\boxed{10}}$

$p\% \ din \ 8=10 \\\\ \frac{p}{100}=\frac{10}{8} \\\\ \frac{p}{100}=\frac{5}{4} \\\\ p= \frac{100*5}{4} \\\\ p= 25*5 \\\\ \boxed{p=125\%}$