Question

O persoana a cheltuit o suma de bani astfel: in prima zi 1 pe 6 din suma, a doua zi 0,(3) din rest si a treia zi 0,25 din noul rest si ramane cu 81 de lei. Care este suma initiala?

Answer 1

x-suma initiala
I zi a cheltuit:           x-x/6=(6x-x)/6=5x/6
0,3=3/9=1/3
II zi a cheltuit:  5x/6-(5x/6)·1/3=5x/6-5x/18=(15x-5x)/18=10x/18=5x/9
0,25=25/100=1/4
III zi a cheltuit:   5x/9-(5x/9)·1/4=5x/9-5x/36=(20x-5x)/36=15x/36=5x/12
5x/12=81
x=(81·12)/5
x=194,4 lei   suma initiala

I zi a cheltuit: 1944/10x1/6=1944/60=32,4 lei
II zi a cheltuit: (194,4-32,4)x1/3=162/3=54 lei
III zi a cheltuit:  (194,4-32,4-54)x1/4=108/4=27 lei
verificare
194,4-32,4-54-27=81 lei ramane

Answer 2

x=suma initiala
x/6=1 zi
x-x/6=5x/6 =rest
5x/6 × 0,(3)= 5x/6 × 1/3=5x/18= a 2-a zi
5x/6-5x/18=(15x-5x) /18=5x/9 =rest
5x/9 ×0,25=5x/9 ×25/100=5x/9 ×1/4=5x/36 = a 3-a zi
x/6+5x/18+5x/36+81=x
6x+10x+5x+2916=36x
15x=2916
x=194,4 lei
in  1 zi  cheltuie  194,4×1/6=32,4 lei
194,4-32,4=162 lei
in  a 2-a zi  cheltuie  162×1/3=54 lei
162-54=108 lei
in  a 3-a zi  cheltuie  108×1/4=27 lei