Răspuns:
2x/3 =3y/5 = 5z/4
x+y+z =1
2x/3 =3y/5 =5z/4 =k
2x/3 = k rezulta ca 2x =3k rezulta ca x = 3k/2
3y/5 = k rezulta ca 3y=5k rezulta ca y=5k/3
5z/4 =k rezulta ca 5z =4k rezulta ca z=4k/5
Cum x+y+z =1 rezulta ca 3k/2 + 5k/3 +4k/5 =1
[tex]\frac{3k}{2 }+\frac{5k}{3}+\frac{4k}{5} =1\\numitorul comun este 30\\\frac{3k*15}{30}+\frac{5k*10}{30} +\frac{4k*6}{30}=30/30\\45k+50k+24k=30\\119k =30\\k =30/119[/tex]
[tex]x= 3k/2 rezulta \\x= 3* \frac{\frac{30}{119} }{2}\\x= 3* \frac{30}{119}*\frac{1}{2}\\x= 3*\frac{30}{238}\\x= 90/238\\[/tex]
[tex]y =5k /3 rezulta\\y = 5*\frac{\frac{30}{119} }{3} \\\\y= 5* \frac{30}{119}*\frac{1}{3} \\y = \frac{150}{357} \\y= 50/119[/tex]
[tex]z=4k/5 rezulta\\z= 4* \frac{\frac{30}{119} }{5}\\z= 4*\frac{30}{119}*\frac{1}{5}\\z= 4* \frac{6}{119}*1\\z= 24/119[/tex]
Explicație pas cu pas:
