Question

o suma de bani a fost cheltuita in felul urmator : prima data 0,2 din toata suma , a doua oara 0,1(6) din ce a ramas , iar a treia oara 1/15 din rest . Stiind ca a ramas necheltuita suma de 28 000 lei se cere sa se afle care a fost suma initiala

Answer 1

x=suma
0,2x=2x/10 1 data
x-2x/10=8x/10=rest
0,1(6)=16-1/90=15/90=1/6
8x/10 × 1/6=4x/5× 1/6=4x/30 = a 2-a data
8x/10-4x/30=(24x-4x) /30=20x/30=2x/3 rest
2x/3 × 1/15 = 2x/45 = a 3-a data
2x/10+4x/30+2x/45+28000=x
18x+12x+4x+2520000=90x
56x=2520000
x=45000 lei

verificare
45000 ×0,2=9000
45000-9000=36000
36000 x 1/6=6000
36000-6000=30000
30000 ×1/15=2000
30000-2000=28000

Answer 2

x suma totala
prima data: 2/10*x=x/5
a doua oara: (16-1)/90*(x-x/5)=15/90*(5x-x)/5=1/6*4x/5=2x/15
a treia oara: 1/15*(x-x/5-2x/15)=1/15*(15x-3x-2x)/15=1/15*10x/15=2x/45
x=x/5+2x/15+2x/45+28000
45x=9x+6x+2x+1260000
45x=17x+1260000
45x-17x=1260000
28x=1260000
x=1260000/28
x=45000