Question

acum doua luni o tableta costa 1000 de lei. Acum o luna pretul tabletei s-a micsoratcu p% iar astazi dupa ce tableta s-a mai ieftinit din nou cu p% ea costa 640 de lei . Afla procentul p%

Answer 1

$p\% \ din \ 1000= \frac{p}{\not100}*\not1000 \to p*10= 10p-reducerea \\\\\\ 1000-10p=10(100-p)-noul\ pret \\\\\\ p\% \ din \ 10(100-p)=\frac{p}{\not 100}*\not 10(100-p)= \frac{p(100-p)}{10}-noua \ reducere \\\\\\ 10(100-p)^{(10}-\frac{p(100-p)}{10}= 100(100-p)-p(100-p)-noul \ nou \ pret \\\\\\ (100-p)(100-p)=640 \\\\ (100-p)^2=640 \\\\ \sqrt{(100-p)^2}=\sqrt{640} \\\\ 100-p=8\sqrt{10} \\\\ 100-8\sqrt{10}=p \\\\ 100-8*3,16=p \\\\ 100-25,29=p \\\\ \boxed{p=74,71 \% }$