Question

Un elev a cheltuit o suma de bani astfel: prima data 0,(4) din intreaga suma a doua oara 30% din rest plus 50 lei, a treia oara 40% din noul rest si inca 60 lei, iar a patra oara ultimii 750 lei. Care a fost suma initiala?

Answer 1

x-suma de bani

0,(4)= 4/9

4/9 din x= 4/9*x= 4x/9 - cat a cheltuit prima data

x-4x/9=(aducem la acelasi numitor)=(9x-4x)/9=5x/9 -restul

30% din 5x/9= 30/100*5x/9= 3/10 * 5x/9= 1/2 * x/3= x/6

x/6 + 50 - cat a cheltuit a 2a oara

5x/9 - (x/6+50)=(aducem la acelasi numitor) = (10x-3x-50*18)/18= (7x-900)/18 -noul rest 

40% din (7x-900)/18=40/100 * (7x-900)/18= 4/10 * (7x-900)/18= 2/5 * (7x-900)/18= 1/5 * (7x-900)/9= (7x-900)/45

(7x-900)/45+60 = (7x-900+2700)/45= (7x+1800)/45 - a cheltuit a3a oara

(7x-900)/18 - (7x+1800)/45=(aducem la acelasi numitor)=

=(35x-4500 -14x-3600)/90=(21x-8100)/90 -noul nou rest

(21x-8100)/90=750

21x-8100=67500

21x=67500+8100
21x=75600

x=75600/21

x=3600-suma initiala