Question

Determina numerele nationale x,y si z, stiind ca intre multimile de mai jos exista o proportionalitate directa:

a) {4,6,7} si {x,y,14}


b) {4,x,16,18} si {y,21,24,z}


c) {x,y,z} si {4,10,15} si 3x-y+2z=45


d) {x,y,z} si {2,3,10} si 5x+5y-2z=1,5

Answer 1

a) 4/x=6/y=7/14

4/x=k rezulta ca x=4/k

6/y=k rezulta ca y=6/k

7/14=k rezulta ca k=1/2

x=4*1/2 rezulta ca x=2

y=6*1/2 REZULTA ca y=3

Answer 2

4/x=6/y=7/14
4*14=7*x
X=8
6*14=y*7
Y=12
b. 4/y=x/21=16/24=18/z
4*24=16y
Y=6
16*21=24x
X=14
16z=24*18
Z=27
c. X/4=y/10=z/15=k
X=4K
Y=10k
Z=15k
3*4k-10k+2*15k=45
32k=45
K=45/32
X=45/8
Y=225/16
Z=15*45/32
d. X/2=y/3=z/10=k
X=2k
Y=3k
Z=10k
10k+15k-20k=1,5
5k=3/2
K=3/10
X=3/5
Y=9/10
Z=3