Question

sorin trage la tinta de 100 de ori. pentru fiecare nereusita obtine 5 puncte, iar pentru fiecare nereusita pierde 4 puncte. cate puncte acumuleaza sorin daca are 10 nereusite? Cate puncte acumuleaza Sorin daca nr.nereusitelor reprezinta un sfert din cel al reusitelor? Cate nereusite are Sorin, stiind ca a acumulat 455 de puncte?

Answer 1

$\hbox{Rezolvarea la ultima intrebare este:} \\\\ x \to nr. \ reusitelor \\ y \to nr. \ nereusitelor \\\\ x+y=100 \ \ \ |*4\\ 5x-4y=455 \\\\\\ 4x+4y=400 \\ 5x-4y=455 \\ ========= (+) \\ 9x \ / \ \ = 855 \ \ \ |:9 \\\\ \boxed{ x=95 \ reusite} \\\\ y=100-95 \\\\ \boxed{y=5 \ nereusite} \\\\\\ \hbox{Rezolvarea pentru a2a intrebare este:} \\\\ x+y=100 \\\\ y=\frac{1}{4} \ din \ x=\frac{1}{4} * x \to \frac{x}{4} ===\ \textgreater \ \underline{ x=4y} \\\\\\ 4y+y=100 \\\\ 5y=100 \ \ \ |:5 \\\\ \boxed{y=20 \ nereusite} \\\\ x=4*20$

$\boxed{x=80 \ reusite} \\\\\\ \hbox{Rezolvarea pentru prima intrebare este:} \\\\ x+y=100 \\\\ 5x-4y= n \\\\ n \to nr. \ de \ puncte \ acumulate \\\\\\ y=10 \ \ \ ===\ \textgreater \ x=100-10 \longrightarrow \boxed{x=90 \ reusite} \\\\\\ n=5*90-4*10 \\\\ n=450-40 \\\\ \boxed{n=410 \ puncte}$