Question

Stiind ca 2x/3 = 3y/5 = 2z/ si ca x+y+z = 1 determina numerele x , y ,z

Ex 6 va rogg
Clasa 6 ​

Answer 1

Răspuns:

$\frac{2x}{3} = \frac{3y}{5} = \frac{5z}{4} \\x+y+z =1 (1)\\\\\frac{3y}{6} = \frac{2x}{3} => 3y = \frac{2x*5}{3} => y = \frac{10x}{9} (2)\\\frac{2x}{3}=\frac{5z}{4} => z = \frac{2x*4}{3*5}=\frac{8x}{15} (3)\\\\din 2 si 3 => 1\\\\x+ \frac{10x}{9} + \frac{8x}{15} =1 <=> \frac{45x +50x+24x}{45}= 1 => 119x = 45 => x= \frac{49}{119}\\y=\frac{10x}{9}=\frac{10*\frac{45}{119} }{9} = \frac{50}{119}\\\\z= \frac{8*\frac{43}{119} }{15} = \frac{24}{119}$

Explicație pas cu pas: