Răspuns :
[tex]x+y+z=1 \\ \frac{x}{0,1} = \frac{y}{2/5} = \frac{z}{1/3} = \frac{x+y+z}{0,1+2/5+1/3} = k \\ 0,1+\frac{2}{5}+\frac{1}{3}= \frac{1,5}{15} + \frac{6}{15} + \frac{5}{15} = \frac{1,5+11}{15} = \frac{12,5}{15} \\ \frac{x+y+z}{12,5/15} = \frac{1}{1} : \frac{12,5}{15} = \frac{1}{1} \cdot \frac{15}{12,5} = \frac{15}{12,5} \\ k= \frac{15}{12,5} \\ x=0,1 \cdot k=0,1 \cdot \frac{15}{12,5} = \frac{1,5}{12,5} \\ \boxed{\bold{x=0,012}} \\ y= \frac{2}{5} \cdot k=\frac{2}{5} \cdot \frac{15}{12,5}= \frac{30}{62,5} [/tex]
[tex]\boxed{\bold{y=0,48}} \\ z= \frac{1}{3} \cdot \frac{15}{12,5}= \frac{15}{37,5} \\ \boxed{\bold{z=0,4}}[/tex]
[tex]\boxed{\bold{y=0,48}} \\ z= \frac{1}{3} \cdot \frac{15}{12,5}= \frac{15}{37,5} \\ \boxed{\bold{z=0,4}}[/tex]
d.p
{x, y, z} ______ > {0,1; 2/5; 1/3}=>x/10=2y/5=z/3=k
x/10=k=>x=10k
2y/5=k=>y=5k/2
z/3=k=>z=3k
10k+5k/2+3k=1
20k+5k+6k=2
k(20+5+6)=2
k*31=2
k=2/31
=>x=10*2/31=20/31
y=5*2/31/2=5/31
z=3*2/31 =6/31
i.p
B) {x, y, z, t}______> {1/2; 1/2; 0,4; 0,2}=>x/2=y/2=2z/5=t/5=k
x/2=k=>x=2k
y/2=k=>y=2k
2z/5=k=>z=5k/2
t/5=k=>t=5k
2k+2k+5k/2+5k=5
k(4+4+5+10)=10
k=10/23
x=2*10/23=20/23
y=2*10/23=20/23
z=5*10/23/2=50/23*1/2=25/23
t=5*10/23=50/23
{x, y, z} ______ > {0,1; 2/5; 1/3}=>x/10=2y/5=z/3=k
x/10=k=>x=10k
2y/5=k=>y=5k/2
z/3=k=>z=3k
10k+5k/2+3k=1
20k+5k+6k=2
k(20+5+6)=2
k*31=2
k=2/31
=>x=10*2/31=20/31
y=5*2/31/2=5/31
z=3*2/31 =6/31
i.p
B) {x, y, z, t}______> {1/2; 1/2; 0,4; 0,2}=>x/2=y/2=2z/5=t/5=k
x/2=k=>x=2k
y/2=k=>y=2k
2z/5=k=>z=5k/2
t/5=k=>t=5k
2k+2k+5k/2+5k=5
k(4+4+5+10)=10
k=10/23
x=2*10/23=20/23
y=2*10/23=20/23
z=5*10/23/2=50/23*1/2=25/23
t=5*10/23=50/23