Question

determinati numerele x si y stiind ca :

a) x supara 2 =y supra 11= z supra 7 si x +y+z=80

b)x/6=y/7=z/8 si x+y-z=20

c)x/5=y/3=z/7 si x+2y-z=192

d)x/14=y/11=z/12 si x+y-z =39

Answer 1

$\frac{x}{2} = \frac{y}{11} = \frac{z}{7} = k \\ x + y + z = 80 \\ x = 2k \\ y = 11k \\ z = 7k \\ 2k + 11k + 7k = 80 \\ 20k = 80 \\ k = 80 \div 20 \\ k = 4 \\ x = 2 \times 4 = 8 \\ y = 11 \times 4 = 44 \\ z = \times 4 = 28$


$\frac{x}{6} = \frac{y}{7} = \frac{z}{8} = k \\ x + y - z = 20 \\ x = 6k \\ y = 7k \\ z = 8k \\ 6k + 7k - 8k = 20 \\ 5k = 20 \\ k = 20 \div 5 \\ k = 4 \\ x = 6 \times 4 = 24 \\ y = 7 \times 4 = 28 \\ z = 8 \times 4 = 32$

$\frac{x}{5} = \frac{y}{3} = \frac{z}{7} = k \\ x + 2y - z = 192 \\ x = 5k \\ y = 3k \\ z = 7k \\ 5k + 2 \times 3k - 7k = 192 \\ 11k - 7k = 192 \\ 4k = 192 \\ k = 192 \div 4 \\ k = 48 \\ x = 5 \times 48 = 240 \\ y = 3 \times 48 = 144 \\ z = 7 \times 48 = 336$

Pe d te las sa il faci sigur/a. Este asemanator cu b doar ca sunt schimbate numerele!!
Succes!!!