Question

Dupa 2 scumpiri succesive cu 20 % un obiect ajunge sa coste 576 lei.Care a fost pretul initial al obiectului?

Answer 1

x = pretul initial
20/100 · x/1 = x/5 lei prima scumpire
x/1+x/5 = 6x/5 ( numitorul comun e 5 ) - noul pret
20/100 · 6x/5 = 6x/25
x/1 + x/5 + 6x/25 = 576/1
25x/25 + 5x/25 + 6x/25 = 14400/25 / ·25
25x + 5x + 6x=14400
36x = 14400 / : 36
x = 400 lei

Answer 2

$x\to \ pretul \ initial \\\\ 20\% \ din \ x \to \frac{20}{100}*x= \frac{1}{5}*x\to \frac{x}{5} -prima \ scumpire \\\\ x^{(5}+\frac{x}{5}=\frac{5x+x}{5}\to \frac{6x}{5}-noul \ pret \\\\ 20\% \ din \ \frac{6x}{5}= \frac{20}{100}*\frac{6x}{5}=\frac{1}{5}*\frac{6x}{5}\to\frac{6x}{25}-a \ doua \ scumpire \\\\ \frac{6x}{5}^{(5}+\frac{6x}{25}= \frac{30x+6x}{25}\to \frac{36x}{25}-noul \ nou \ pret \\\\ \frac{36x}{25}=576 \\\\ x=\frac{25*576}{36} \\\\ x=25*16 \\\\ \boxed{x=400}$