in prima luna cheltuie [tex] \frac{2}{3}x [/tex]
in a doua luna cheltuie 2 treimi din rest [tex] \frac{2}{3} (x- \frac{2}{3}x)[/tex]
in a 3a luna inca 2 treimi din ce a ramas de data asta:
[tex]\frac{2}{3}[x-\frac{2}{3}x-\frac{2}{3} (x- \frac{2}{3}x)][/tex]
simplu nu? sigur ca da, sa scadem:
[tex]x- \frac{2}{3}x - \frac{2}{3} (x- \frac{2}{3}x) - \frac{2}{3}[x-\frac{2}{3}x-\frac{2}{3} (x- \frac{2}{3}x)] = 1123[/tex]
desfacem parantezele:
[tex]x- \frac{2}{3}x-\frac{2}{3}x+\frac{4}{9}x-\frac{2}{3}x+\frac{4}{9}x+\frac{4}{9}x-\frac{8}{27}x = 1123
[/tex]
aducem la acelasi numitor:
[tex] \frac{27x-18x-18x+12x-18x+12x+12x-8x}{27} = 1123 [/tex]
adica
[tex] \frac{x}{27} =1123[/tex]
adica x=1123 * 27 = 30321
inseamna ca in cele 3 luni a cheltuit 30321-1123 = 29198 lei
