Question

1. determinaţi numerele x, y si z invers proportionale cu numerele 1,5;2,5; si 3,5 stiind ca x+2y+3z=244

Answer 1

$1.5 = \frac{3}{2}$

$2.5 = \frac{5}{2}$

$3.5 = \frac{7}{2}$

$(x, y , z) \: ip \: \: ( \frac{3}{2}... \frac{5}{2} ... \frac{7}{2} )$

$x \times \frac{3}{2} = y \times \frac{5}{2} = z \times \frac{7}{2} = k$

$\frac{3x}{2} = \frac{5y}{2} = \frac{7z}{2} = k$
$\frac{3x}{2} = k = > x = \frac{2k}{3}$
$\frac{5y}{2} = k = > y = \frac{2k}{5}$
$\frac{7z}{2} = k = > z = \frac{2k}{7}$
**x+2y+3z=244
$\frac{2k}{3} + 2 \times ( \frac{2k}{5}) + 3 \times ( \frac{2k}{7} ) = 244$
$\frac{2k}{3} + \frac{4k}{5} + \frac{6k}{7} = 244$
**aduci la numitor comun(care e 105) si scapi de numitor
70k+84k+90k=25620
244k=25620
$k = \frac{25620}{244}$
k=105
***************
$x = \frac{2 \times 150}{3 } = 2 \times 5 0= 100$

$y = \frac{2 \times 150}{5} = 2 \times 30 = 60$

$z = \frac{2 \times 150}{7} = \frac{300}{7}$