Question

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

Answer 1

fie x suma initiala, vom scrie in functie de x cat a cheltuit Bogdan in fiecare zi:

I) 1/3x+180

II) 1/3[x-(1/3x+180)]+180=2/9x+120

III) 1/3[x-(2/9x+120)]+180=7/27x+140

stiind suma ramasa obtinem ecuatia:

x-(1/3x+180)-(2/9x+120)-(7/27x+140)=480

x-1/3x-2/9x-7/27x-440=480

5/27x=920 => x=920x27/5=4968

x=4968 lei => I) 1/3x+180=1836 lei

                     II) 2/9x+120=1224 lei

                     III) 7/27x+140=1428 lei