Question

a)x/6=y/7=z/8
x+y-z=20
b)x/5=y/3=z/7
x+2y-z=192
c) x/14=y/11=z/12
x+y-z=39
va rog frumos

Answer 1

6k+7k-8k=20
k=4
x=24
y=28
z=32
b) 5k+6k-7k=192
4k=192
k=48
x=240
y=144
z=336
c)14k+11k-12k=39
13k=39
k=3
x=42
y=33
z=36

Answer 2

$a) \: \frac{x}{6} = \frac{y}{7} = \frac{z}{8}$
$x = \frac{6y}{7}$
$z = \frac{8y}{7}$
$\frac{6y}{7} + y - \frac{8y}{7} =20$
$= > 6y + 7y - 8y = 140$
$=> 5y = 140 \\ y = \frac{140}{5} \\ y = 28 \\ x = 24 \\ z = 32$
$b) x = \frac{5y}{3} \\ z = \frac{7y}{3} \\ \frac{5y}{3} +2y - \frac{7y}{3} = 192 \\ = > 5y + 6y - 7y = 576 \\ => 4y = 576 \\ y = 144 \\ x = 240 \\ z = 336$
$c) x = \frac{14y}{11} \\ z = \frac{12y}{11} \\ \frac{14y}{11} +y - \frac{12y}{11} = 429 \\ = > 14y + 11y - 12y = 429 \\ => 13y = 429 \\ y = 33 \\ x = 42 \\ z = 26$