Răspuns:
1. a) [tex]\frac{b}{a} = \frac{36}{45} = \frac{3*12}{3*15}[/tex]= [tex]\frac{3*4}{3*5} = \frac{4}{5}[/tex]
b) a= [tex]\frac{5b}{3}[/tex]
c) 2x=8*7 x= 56:2= 28 x=28
2.a) [tex]\frac{a}{3} =5[/tex]=> a= 3*5= 15 a=15
[tex]\frac{b}{4} =5[/tex] => b= 4*5=20 b=20
a+b= 15+20=35 a+b=35
b) 6x= 15*7 x= 3*5*7: 2*3= 35:2= 17.5 x= 17.5
c) 200*60:100=120
200+120 = 320 dupa scumpire
3. a) [tex]\frac{x}{2} = \frac{z}{4}[/tex] => x= 2*6:4= 12:4= 3 x=3
[tex]\frac{y}{3} =\frac{z}{4}[/tex]=> y= 3*6:4= 18:4 =4.5
x+y= 3+4.5= 7.5
b) a*3=b*4 a+b=14 a= b*4:3
[tex]\frac{4b}{3}[/tex]+b= 14 4b+3b= 14*3 7b= 14*3 b= 14*3:7 =2*3=6
b=6 a= 6*4:3=24:3= 8 a=8
c) [tex]\frac{40x}{100} =6[/tex] x= 6*100:40= 600:40=15 x= 15
4. [tex]\frac{x}{4} = \frac{y}{5} =\frac{z}{7}[/tex] x+y+z= 64
x= [tex]\frac{4y}{5}[/tex] z= [tex]\frac{7y}{5}[/tex] [tex]\frac{4y}{5} + y+ \frac{7y}{5}[/tex]=64 aducem la acelasi numitor
4y+7y+5y= 64*5 16y= 64*5 y= 64*5:16 = 4*5=20 y=20
x= 4*20:5= 4*4=16 x=16
z= 7*20:5= 7*4=28 z=28
5. [tex]\frac{x}{2} =\frac{y}{6}[/tex] 2y=6x y=3x
[tex]\frac{4x+6y}{x+y}[/tex]= [tex]\frac{4x+6*3x}{x+3x}[/tex]= [tex]\frac{4x+18x}{4x}[/tex]= [tex]\frac{22x}{4x}[/tex] = [tex]\frac{11}{2}[/tex]
7.
4*(4x-2y)= 1*(2x-y)
16x-8y= 2x-y 16x-2x= 8y-y 14x=7y /:7
y=2x [tex]\frac{x}{y}[/tex]= 2
