Question

Media aritmetica a numerelor a si b este 2,8 ,media aritmetica a numerelor a si c este egala cu 3,5 ,iar media aritmetica a numerelor b si c este egala cu 3,9. Determinati numerele a,b,c.

Answer 1

2,8⇔28/10⇒(a+b)/2=28/10⇔10(a+b)=2×28⇔10(a+b)=56⇒a+b=56/10⇒a=56/10-b si b=56/10-a
3,5⇔35/10⇒(a+c)/2=35/10⇔10(a+c)=35×2⇔10(a+c)=70⇔a+c=70/10⇔a+c=7⇒c=7-a
3,9=39/10⇒(b+c)/2=39/10⇔10(b+c)=39×2⇔10(b+c)=78⇒(b+c)=78/10⇒b=78/10-c
a=56/10-b iar b=78/10-c⇒a=56/10-(78/10-c)⇒a=56/10-78/10+c⇒a=-22/10+c⇒c=a+22/10
acum avem
a+c=7 si c=a+22/10⇒a+a+22/10=7⇔2a+22/10=7⇔2a=7-22/10⇔2a=70/10-22/10⇔2a=48/10⇒a=48/10:2⇒a=48/10×1/2⇒a=24/10
acum avem a=24/10 si c=7-a⇒c=7-24/10⇒c=70/10-24/10⇒c=46/10
avem c=46/10 si b=78/10-c⇒b=78/10-46/10⇒b=32/10
verificare
(a+b)/2=(24/10+32/10)/2=56/10/2=56/10:2=56/10×1/2=56/20=2,8⇔20/10
(b+c)/2=(32/1046/10)/3=78/10/2⇔78/10×1/2=78/20=3,9⇔39/10
(a+c)/2=(24/10+46/10)/2=70/10/2⇔70/10×1/2=7/2=3,5⇔35/10