Question

1. Dacă 2x/5y =3/8 si x+y =93 aflați x si y
2. Dacă a/2=b/4=c/6 si a+2c=7 aflați a,b si c
3.Determinați nr. x,y si z stiind ca x/2 =y/3=z/4 Si 2x+y+5z=81

Answer 1

1.  2x/5y=3/8=> 8 ori 2x=3 ori 5y=>16x=15y=> x=15y/16
x+y=93
15y/16+y=93
15y/16+16y/16=93
31y/16=93=>y=16 ori 93/31
                    y=48
x=15 ori 48/16
x=45

2.    a/2=b/4=c/6

a+2c=7
a/2=c/6=>a=2c/6 care se sim plifica cu 2=>a=c/3
c/3+2c=7
c/3+2 ori 3c/3=7
c/3+6c/3=7
7c/3=7=>c=3 ori 7/7=>c=3
a+2 ori 3=7
a+6=7=.a=1
a/2=b/4 dar a=1
1/2=b/4=> b=4/2=>b=2

3. x/2=y/3=z/4
2x+y+5z=81
x/2=y/3=> x=2y/3
2 ori 2y/3+y+5z=81
4y/3+y+5z=81
y/3=z/4=>y=3z/4
4 ori 3z/4/3+3z/4+5z=81
12z/4/3+3z/4+5z=81
12z/4:3+3z/4+5z=81
12z/4 ori 1/3+3z/4+5z=81
12z/12+3z/4+5z=81
z+3z/4+5z=81
6z+3z/4=81
6z ori 4/4+3z/4=81
24z/4+3z/4=81
27z/4=81=>z=81 ori 4/27=>z=12
                                            y=3z/4=>y=  3 ori 12/4=>y=9
                                             x=2y/3=>x=2 ori 9/3=>x=6