Question

Aflati cinci numere rationale stiin ca primele trei sunt direct proportionale cu 5, 6 si 10, ultimele 3 sunt d.p. cu 3, 8, 12 si suma lor este egala cu 200
(Poate ca gasiti ciudat faptul cane cere 5 numere cand ne da sase, dar asa scrie in carte)

Answer 1

a+b+c+d+e+f=200
a=5k
b=6k
c=10k
d=3k
e=8k
f=12k

5k+6k+10k+3k+8k+12k=200
44k=200
k=200/44
k=50/11

a=5*50/11
a=250/11
b=6*50/11
b=300/11
c=10*50/11
c=500/11
d=3*50/11
d=150/11
e=8*50/11
e=400/11
f=12*50/11

Sigur pe undeva e o greseala. Dar asta e modul de rezolvare.

Answer 2

a/5=b/6=c/10=k1 ⇒ a=5k1, b=6k1, c=10k1
c/3=d/8=e/12=k2 ⇒c=3k2, d=8k2, e=12k2
egalez pe c
10k1=3k2 ⇒ k2=10/3*k1
stiu ca a+b+c+d+e=200
5k1+6k1+10k1+8*10/3*k1+12*10/3*k1=200
Aduc la acelasi numitor in stanga si in dreapta egalului
21*3*k1+80k1+120k1=600
263k1=600 ⇒ k1=600/263 ⇒ a=3000/263, b=3600/263, c=6000/263. d=48000/789, e=72000/789