Question

Determinati numerele x,y si z invers proportionale cu numerele 1,5; 2,5 si 3,5 daca x+2y+3z=244

Answer 1

x+2y+3z=244
x ori 1,5 = y x 2,5 = z x 3,5 = k
x ori 1, 5= k => x= k : 1, 5 = > x= 2k/3 (am facut simplificari, am calculat)
y x 2,5= k => y= k : 2, 5 => x= 2k/5
zx 3, 5=k => z = k : 3,5 => z= 2k/7
inlocuim:
2k/3 + 2 x 2k/5 + 3x 2k/7= 244
acum aducem la acelasi numitor (105)
70k+ 84k + 90k(totul supra 105) = 244
244k/105=244
244k= 244 x 105
k= 244 x 105 (totul supra 244 ,iar apoi simplificam 244 cu 244)
k= 105
x= 105x2 / 3 =.> x= 70
y= 2x 105 / 5 => y= 42
z= 2 x 105/ 7=> z= 30