Question

plase help me!
1)
{a,b,c}direct proporțional {4,5,6}
a+b+c=75

2)
{x,y,z} direct proporțional {3,4,6}
( x+y+z):2=65​

Answer 1

Rezolvare:

a)

$\frac{a}{4}=\frac{b}{5}=\frac{c}{6} = k => a = 4k; b = 5k; c = 6k \\a + b + c = 75\\= > 4k + 5k + 6k = 75 => 15k = 75 => k = 5 => a = 20; b = 25; c = 30$

Proba: 20 + 25 + 30 = 75 ✔️

b)

$\frac{x}{3} = \frac{y}{4} = \frac{z}{6} = k => x = 3k; y = 4k; z = 6k \\(x + y + z) : 2 = 65 => 13k : 2 = 65 => k = \frac{65*2}{13} = \frac{130}{13} = 10 \\=> k = 10 => x = 30; y = 40; z = 60$

Proba: (30 + 40 + 60) : 2 = 130 : 2 = 65 ✔️