Question

Suma a trei nr este 1.Sa se afle numrele stiind ca sunt direct proportionale cu 1supra3,2supra5,si 0,1.

Answer 1

Notez cu a, b, c-numerele.
{a, b, c} d.p {1/3; 2/5; 1/10}           [0,1=1/10]
$\frac{a}{3}= \frac{2b}{5}= \frac{c}{10}$
$a= \frac{3*2b}{5}= \frac{6b}{5}$
$c= \frac{10*2b}{5}=4b$
$\frac{6b}{5}+b+4b=1$
[tex]6b+5b+20b=5 [/tex]
$31b=5$
$b= \frac{5}{31}$
a=6*5/31/5=6/31
c=4*5/31=20/31

Answer 2

( / inseamna linie de fractie) 0.1=1/10
{a,b,c} d.p. { 1/3;2/5;1/10} ⇒a/1/3=b/2/5=c/1/10=k
a+b+c=1
daca a/1/3=k⇒a=k·1/3⇒a=k/3
         b/2/5=k⇒b=2k/5
         c/1/10=k⇒c=k/10
Inlocuiesti in a relatia de adunare si obtii:
k/3+2k/5+k/10= 1
aduci la acelas numitor (30)
10k/30+12k/30+3k/30=30/30
Se elimina numitorul si obtinem ca
25k=30
k=30/25, simplificam, k= 6/5
Inlocuim
a=6/5 · 1/3 = 2/5
b=6/5 · 2/5=12/25
c=6/5 · 1/10=6/50

Verificam:
2/5+12/25+6/50= 20/50+24/50+6/50=50/50=1