Question

5. Aflati toate numerele de forma abc , care impartite la bc dau catul 5 si restul 6xc​

Answer 1

Explicație pas cu pas:

abc= 5bc+6c

100a+10b+c= 5(10b+c)+6c

100a+10b+c= 50b+5c+6c

100a-40b-10c= 0/:10

10a-4b+c= 0,

10a, 4b sunt nr. pare, deci c trebuie sa fie par

c= 0, 10a= 4b/:2, 5a=2b, a=2, b= 5

abc= 250,

c=2, 10a-4b+2= 0/:2, 5a-2b+1= 0, a=1, b= 3

abc= 132

5a-2b+1= 0, a= 3, b=8,

abc= 282

c=4, 10a-4b+4=0/:2, 5a-2b+2= 0

a= 2, b= 6

abc= 264

c=6, 10a-4b+6=0/:2* 5a-2b+3=0

a= 1, b= 4

abc= 146

a=3, b= 9

abc= 396

c=8, 10a-4b+8=0/:2, 5a-2b+4= 0

a= 2, b= 7

abc= 278