Question

Trei persoane au depus la banca sume direct proportionale cu 4, 6 si 14.Dobanda oferita de banca este de 8% pe an. Dupa un an aveau la banca in total 9072 lei.
a) Ce suma de bani a depus initial fiecare persoana?
b) Ce suma de bani avea in banca dupa un an fiecare persoana?
c) Ce procent reprezinta suma celei de-a treia persoane din suma sumelor primelor doua persoane dupa un an?

Answer 1

(a+b+c)+(a+b+c)x8/100=9072

{a,b,c}dp{4,6,14}
a/4=b/6=c/14=k
a/4=k⇒a=4k
b/6=k⇒b=6k
c/14=k⇒c=14k
inlocuim in I relatie
(4k+6k+14k)+(4k+6k+14k)x8/100=9072
24k+24kx8/100=9072
24k+48k/25=9072
(24kx25+48k)/25=9072
648k=9072x25
k=226800/648
k=350
a=4k=4x350=1400
b=6k=6x350=2100
c=14k=14x350=4900
a) prima persoana a depus 1400 lei
II pers:2100 lei
III pers:4900 lei

b) dupa un an aveau in banca:
I pers : 1400+1400x8/100=1400+112=1512 lei
II pers: 2100+2100x8/100=2100+168=2268 lei
III pers: 4900+4900x8/100=4900+392=5292 lei
1512+2268+5292=9072 lei

c)p/100x5292=1512+2268
5292p/100=3780
5292p=3780x100
p=378000/5292
p=71,42....≈71%