Question

determinati numerele a,b,c direct proportionale cu 3,4,5 daca a+2b+3c=78 si b) determinati numerele naturale x,y,z stiind ca sunt invers proportionale cu 0,5, o,(3); si o,25 si x+y+z=36

Answer 1

a)a,b,c d.p 3,4,5 => a/3=b/4=c/5=K
Astfel incat a=3K
b=4K
c=5K
a+2b+3c=78
26K=78 => K=3
a=9
b=12
c=15

b)x,y,z i.p 1/2 , 1/3 , 1/4
=> x/2=y/3=z/4=L
x=2L
y=3L
z=4L
x+y+z=36 => 9L=36
L=36/9=4
x=8
y=12
z=16

Answer 2

a=3k
b=4k
c=5k
3k+2*4k+3*5k=78
3k+8k+15k=78
26k=78
k=3
a=3k=3*3=9
b=4k=4*3=12
c=5k=5*3=15

b)
0,5=5/10=1/2
0,(3)=3/9=1/3
0 ,25=25/100=1/4
x/(1/0,5)=k   ⇒ x=2k
y/[1/0,(3)]=k ⇒ y=3k 
z/(1/0,25]=k ⇒ y=4k 
x+y+z=36
2k+3k+4k=36
9k=36
k=4
x=2*4=8
y=3*4=12
z=4*4=16