Question

Care sunt numerele consecutive care dau suma 100. Aflati numerele.
Ma puteti ajuta ?

Answer 1

daca avem :

2 nr.consecutive => x+(x+1) = 100                   =>x=(100-1):2∉N

3 nr.consecutive => x+(x+1)+(x+2) =100          =>x=(100-3):3∉N

4 nr.consecutive => x+(x+1)+(x+2)+(x+3)=100 =>x=(100-6):4∉N

5 nr.consecutiva =>x+(x+1)+(x+2)+(x+3)+(x+4)=100

                                                                           =>x=(100-10):5=18

     inseamna ca numerele sunt: 18+19+20+21+22 = 100

Answer 2

a) 2 numere consecutive⇒ a si b unde b=a+1; 

a+(a+1) = 100   ⇒a=(100-1):2=99:2  nu apartine multimii nr naturale

b) 3 numere consecutive ⇒a, b=a+1, c=a+2

 a+(a+1)+(a+2) =100  ⇒3a+3=100⇒ 

⇒a=(100-3):3=97:3 nu apartine multimii nr naturale

c) 4 numere consecutive ⇒a, b=a+1, c=a+2, d=a+3

 a+(a+1)+(a+2)+(a+3)=100 ⇒4a+6=100, a=(100-6):4=94:4  nu apartine multimii nr naturale

d) 5 numere consecutive⇒a, b=a+1, c=a+2, d=a+3, e=a+4

a+(a+1)+(a+2)+(a+3)+(a+4)=100⇒5a+10=100                                  ⇒5a=(100-10)⇒5a=90⇒a=90:5⇒a=18

  a=18, b=a+1=19, c=a+2=20, d=a+3=21, e=a+4=22

verificare
                 a+b+c+d+e=100
 18+19+20+21+22 = 100
               100=100