Question

La un magazin de paine, la inchidere ,erau 3 persoane ,care au cumparat toata painea care mai era.Sa se afle cate paini au fost,daca fiecare a cumparat jumatate din nr. painilor care se mai gaseau cand i-a venit randul si inca o jum. de paine.Cate paini a a cumparat fiecare persoana? 

Answer 1

x-nr initial de paini

x/2 +1/2 -a cumparat prima persoana

x- (x/2 +1/2)=  x- (x+1)/2=  (2x-x-1)/2=  (x-1)/2 -restul

(x-1)/2/2 +1/2=  (x-1)/2 * 1/2+1/2=  (x-1)/4 +1/2=  (x-1+2)/4=  (x+1)/4-a cumparat a2a persoana.

(x-1)/2 -(x+1)/4=  (2x-2-x-1)/4=  (x-3)/4 -noul rest

(x-3)/4/2 +1/2=  (x-3)/4*1/2 +1/2= (x-3)/8 +1/2=  (x-3+4)/8=  (x+1)/8-a cumparat a3a persoana

(x+1)/2 + (x+1)/4 + (x+1)/8=x  aducem la acelasi numitor

4x+4+2x+2+x+1=8x

7x+7=8x

7x-8x=-7

-x=-7

x=7

(7+1)/2= 8/2=4 paini a cumparat prima persoana

(7+1)/4= 8/4=2 paini a cumparat a2a persoana

(7+1)/8= 8/8=1 paine a cumparat a3a persoana

Answer 2

I x/2+1/2
  rest r1=x/2-1/2
II r1/2+1/2
  rest r2=r1/2-1/2
III r2/2+1/2
   rest r2/2-1/2 = 0 ⇒ r2/2=1/2⇒ r2=1
  1=r1/2-1/2 ⇒ r1/2=1+1/2=3/2⇒ r1=3
  3=x/2-1/2⇒ x=3+1/2= 7/2⇒ x=7
verificare I 7/2+1/2=4 paini
                r1=3
             II 3/2+1/2=2 paini
               r2=1
            III 1/2+1/2=1
               rest 0