Question

Numerele nenule a b si c sunt direct proportionale cu 4,9,5 ,media aritmetica a lor este 90

Answer 1

{a; b; c} d. p. {4; 9; 5}

$\frac{a}{4} = \frac{b}{9} = \frac{c}{5} = k$
a=4k
b=9k
c=5k
$m = \frac{a + b + c}{3}$
$90 = \frac{4k + 9k + 5k}{3}$
270=18k
k=270÷18
k=15

Solutia:
a=4×15=60
b=9×15=135
c=5×15=75

Answer 2

{a, b, c} d.p. {4, 9, 5}

$\it \frac{a}{4} = \frac{b}{9} = \frac{c}{5 } = K \\ \\ \it \frac{a}{4} = K = = > a = 4K \\ \\ \it \frac{b}{9} = K = = > b = 9K \\ \\ \it \frac{c}{5} = K = = > c = 5K \\ \\ \it \frac{a \: + \: b \: + \: c}{3} = 90 = = > a \: + \: b \: + \: c = 90 \cdot 3 = = > a \: + \: b \: + \: c = 270 \\ \\ \it 4K + 9K + 5K = 270 = = > \\ \it 18K = 270 \: = = > \\ \it K = \frac{270}{18} = = > \\ \\ \it K = 15 \\ \it a = 4K = = > a = 4 \cdot 15 = = > a = 60 \\ \it b = 9K = = > b = 9 \cdot 15 = = > b = 135 \\ \it c = 5K = = > c = 5 \cdot 15 = = > c = 75$