Question

Media aritmetica a numerelor x si y este 12,5.Aflati numerele x si y,stiind ca:
a)x este de 4 ori mai mare ca y
b)x reprezinta 0,3 din y
c)x si y sunt direct proportionate cu numerele 2 si 3

Answer 1

a) (x+y)/2=12,5 => (4y+y)/2=12,5 => 5y=25 => y=5 => x=4y=4*5=20
     deci x=20, y=5.
b) (3/10*y+y)/2=12,5 =>13/10*y=25 =>y=25*10/13 =>y=250/13 => x=3/10*y=3/10*250/13=75/13
     deci x=75/13, y=250/13
c) x/2=y/2=k => x=2k, y=3k => (2k+3k)/2=12,5 => 5k=25 => k=5 => x=2k=10, y=3k=15
     deci x=10, y=15

Answer 2

a) $x=4y ; \frac{x+y}{2}=12,5 ; \frac{5y}{2}=12,5 ; 5y=25 ; y=5 ; x=20$
b) $x=0,3*y ; x= \frac{3y}{10} ; \frac{ \frac{3y}{10}+y }{2}= \frac{ \frac{13y}{2} }{2} = \frac{13y}{4}=12,5= \frac{25}{2} ; 13y*2=25*4 ; \\ 13y=50 ; y= \frac{50}{13} ;x= \frac{3}{10}* \frac{50}{13} = \frac{150}{130}= \frac{15}{13}$
c) $\frac{x}{2} = \frac{y}{3} =k ; x=2k ;y=3k ;\frac{x+y}{2}= \frac{5k}{2} =12,5;5k=25;k=5;x=10; \\ y=15$