Question

Bogdan a cheltuit 1/3 din suma pe care o are plus 180 lei in prima zi,in a doua zi 1/3 din rest plus 180lei si a treia zi 1/3 din noul rest plus 180 lei si ii mai raman 480 lei. Cati lei a avut Bogdan si cat a cheltuit in fiecare zi?

Answer 1

x= suma lui Bogdan
{[($\frac{2x}{3}) -180$]·$\frac{1}{3}$-180}·$\frac{1}{3} -180=$480
{[($\frac{2x}{3}) -180$]·$\frac{1}{3}$-180}·$\frac{1}{3}$=480+180
{[($\frac{2x}{3}) -180$]·$\frac{1}{3}$-180}·$\frac{1}{3}$=660
[($\frac{2x}{3}) -180$]·$\frac{1}{3}$-180=660·3
[($\frac{2x}{3}) -180$]·$\frac{1}{3}$-180=1980
[($\frac{2x}{3}) -180$]·$\frac{1}{3}$=1980+180
[($\frac{2x}{3}) -180$]·$\frac{1}{3}$=2160
$\frac{2x}{3} -180$=2160·3
$\frac{2x}{3} -180$=6480
$\frac{2x}{3}$=6480+180
$\frac{2x}{3}$=6660
2x=6660·3
2x=19980
x=19980÷2
x=9990