Question

Impartiti numarul 106 in parti direct proportionale cu numerele 0,(3); 2; 1,2.

Answer 1

x=0,(3)k=3k/9=k/3
x=2k
z=1,2k
k/3+2k+1,2k=106
k+6k+3,6k=318
10,6k=318
k=30
x=k/3=10
x=2k=60
z=1,2k=36

Answer 2

x/3/9=y/2=z/1,2=k
⇒x/3/9=k⇒x/1/3=k⇒x=1/3·k⇒x=k/3;
⇒y/2=k⇒y=2k;
⇒z/1.2=k⇒z/12/10=k⇒z=12/10·k⇒z=12k/10⇒z=6k/5;
⇒x+y+z=106
⇒k/3+2k+6k/5=106
⇒5k/15+30k/15+18k/15=106
⇒[5k+30k+18k]/15=106
⇒53k/15=106
⇒53k=15·106
⇒53k=1590
⇒k=1590/53
⇒k=30;
⇒x=k/3⇒x=30/3⇒x=10;
⇒y=2k⇒y=2·30⇒y=60;
⇒z=6k/5⇒z=6·30/5⇒z=6·6⇒z=36;