Question

As vrea sa-mi rezolvati aceata problema: Pretul unui telefon a cazut cu 10% si,dupa o saptamana,noul pret a cazut inca 10%.Dupa cele doua modificari de ptet telefonu costa 810 lei. a)calculati pretul initial al tlefonuui;
b)cu ce procent din pretu initia s-a micsorat pretul telefonuui dupa cele doua ieftiniri?

Answer 1

$x\to pretul \ initial \\\\ 10\% \ din \ x \to \frac{\not10}{\not100}*x = \frac{1}{10}*x \to \frac{x}{10} - prima \ scadere \\\\ x^{(10}-\frac{x}{10}=\frac{10x-x}{10} \to \frac{9x}{10}-noul \ pret \\\\ 10\% \ din \ \frac{9x}{10} = \frac{\not10}{\not100}* \frac{9x}{10}=\frac{1}{10}*\frac{9x}{10}\to \frac{9x}{100}-a \ doua \ scadere \\\\ \frac{9x}{10}^{(10}-\frac{9x}{100}=\frac{90x-9x}{100}\to \frac{81x}{100}-noul \ nou \ pret \\\\\\ \frac{81x}{100}=810 \\\\ x=\frac{\not810*100}{\not81} \\\\ x=10*100$

$\boxed{x=1000\ lei} \\\\ b) p\% \ din \ 1000=810 \\\\ \frac{p}{\not100}*\not1000=810 \\\\ p*10=810 \\\\ p=\frac{\not810}{\not10} \\\\\ p=81\%\\\\100\% -81\% \Longrightarrow \boxed{19\%-procentul \ dupa \ cele \ 2 \ ieftiniri}$

Answer 2

Pretul il notezi cu x
x-10/100*x=x-x/10=9x/10
9x/10-10/100*9x/10=9x/10-9x/100=81x/100
81x/100=810
81x=81000 deci x=1000 lei
10*1000/100=100 lei prima ieftinire
900-810=90 lei a doua ieftinire
Total 100+90=190 lei
1000p/100=190
1000p=19000 deci p=19%