Question

Aflati numerele x, y,z direct proportionale cu 7, 4 si 9 in urmatoarele situatii
a) x+y+z=100
b) 3x-2y+z=11

Answer 1

{x,y,z}dp{7,4,9}
x/7=y/4=z/9=k
x/7=k⇒ x=7k
y/4=k⇒ y=4k
z/9=k⇒ z=9k
a) x+y+z=100
7k+4k+9k=100
20k=100
k=100/20=5
x=7k=7·5=35
y=4k=4·5=20
z=9k=9·5=45
deci 35+20+45=100
b) 3x-2y+z=11
3·7k-2·4k+9k=11
21k-8k+9k=11
22k=11
k=11/22=1/2
x=7k=7·1/2=7/2=3,5
y=4k=4·1/2=2
z=9k=9·1/2=9/2=4,5

Answer 2

x/7=y/4=z/9=k
x=7k
y=4k
z=9k
7k+4k+9k=100
20k=100 => k=100:20 => k=5
x=35
y=20
z=45

a) 35+20+45=100

b) 3inmultit cu 35-2inmultit cu 20+45

    105-40+45=
     65+45=110 (ai facut o eroare la punctul b) inloc de 11 este 110)