Question

1.Suma a patru numere este 5. Stiind ca ele sunt invers proportionale cu numerele 1/2;1/3;0,4;0,2 aflati numerele
2.Determinati numerele x,y,z stiind ca sunt invers proportionate cu 0,5;0,(3);0,25 si ca x+y+z=36.
3.Determinati numerele a b c stiind ca sunt invers proportionale cu 0,(3);0,5 si 0,25 si ca 6a+2b-5c=50 PLZPLZ urgentttttt 15 pcte

Answer 1

1)
a+b+c+d=5
a/2=b/3=0,4c=0,2d
a/2=b/3=2c/5=d/5    b=3a/2  c=5a/4    d=5a/2
a+3a/2+5a/4+5a/2=5
4a+6a+5a+10a=20
25a=20
a=4/5
b=3/2 *4/5=6/5
c=5/4*4/5=1
d=5/2*4/5=2
verificare  4/5+6/5+1+2=10/5+3=2+3=5


2)
0,5=5/10=1/2
0,(3)=3/9=1/3
0,24=24/100=6/25
x/2=y/3=6z/25    y=3x/2     z=25x/12
x+y+z=36
x+3x/2+25x/12=36
12x+18x+25x=432
x=432/55
y=3/2 *432/55=648/55
z=25/12*432/55=180/11

verificare
432/55+648/55+180/11=(432+648+900)/55=1980/55=36

3)
0,(3)=3/9=1/3
0,5=5/10=1/2
0,25=25/100=1/4
a/3=b/2=c/4    b=2a/3    c=4a/3
6a+2*2a/3-5*4a/3=50
6a+4a/3-20a/3=50
18a+4a-20a=150
2a=150
a=75
b=2*75/3=50
c=4*75/3=100