Question

Numerele naturale x,y,z sunt direct proporționale cu 0,1; 0,2 ;0,3 ,iar 3x+2y+5z=110. Aflați x,y,z

Answer 1

{x,y,z}dp={1/10, 2/10, 3/10}
10x=10y/2=10z/3=k
10x=k⇒x=k/10
5y=k⇒y=k/5
10z/3=k⇒x=3k/10
3x+2y+5z=110
3·k/10+2·k/5+5·3k/10=110
3k/10+2k/5+15k/10=110
18k/10+4k/10=110
22k/10=110
22k=110·10
k=1100/22=550/11
k=50
x=k/10
x=50/10=5
y=k/5=50/5=10
y=10
z=3k/10=3·50/10=15
z=15