Question

Mircea pleaca intr-o excursie de 4 zile. In 1 zi cheltuiieste un sfert din banii de buzunar a 2 zi cheltuieste un sfert din banii ramasi a 3 zi 10 lei pastrandu-si pentru ultima zi jumătate din suma avuta. Cati lei a avut Mircea?

Answer 1

$x \to suma \ initiala \\\\ \frac{1}{4} \ din \ x\to \frac{1}{4} * x = \frac{x}{4} -prima \ zi \\\\ x^{(4} -\frac{x}{4} = \frac{4x-x}{4} \to \frac{3x}{4} -restul \\\\ \frac{1}{4} \ din \ \frac{3x}{4} \to \frac{1}{4}* \frac{3x}{4}= \frac{3x}{16} - a \ doua \ zi \\\\ \frac{3x}{4}^{(4}-\frac{3x}{16}= \frac{12x-3x}{16} \to \frac{9x}{16} -noul \ rest \\\\ \frac{9x}{16}-10^{(16}= \frac{9x-160}{16}- cat \ cheltuit \ a \ 4a \ zi \\\\\\ \frac{9x-160}{16}=\frac{x}{2}^{(8} \\\\ 9x-160=8x \\\\ 9x-8x=160$


$\boxed{x \to 160 \ lei}$