Question

Patru numere sunt direct proportionale cu 0,0(6) , 0,(2) , 0,(3) si 2. Media aritmetica a lor este 42. Aflati numerele. Va rog mult!

Answer 1

0,0(6)=6/90=1/15
0,(2)=2/9
0,(3)=3/9=1/3
2
(k/15+2k/9+k/3+2k)/4=42
k/15+2k/9+k/3+2k=168
6k+20k+30k+180k=15120
236k=15120
59k=3780
k=3780/59
k/15=(3780/59)/15=252/59
2k/9=(3780/59) ×2/9=840/59
k/3=(3780/59)/3=1260/59
2k=(3780/59) 2=7560/59


verificare
(252/59+840/59+1260/59+7560/59)/4=(9912/59)/4=168/4=42