Question

Cifrele a,b,c verifica relatia:
2(ab+c)=3(ab-c).Calculati suma tuturor numerelor de forma abc(cu liniuta deasupra) ale caror cifre verifica relatia de mai sus.

Answer 1

2(10a+b+c)=3(10a+b-c)
20a+2b+2c=30a+3b-3c
2c+3c=30a-20a+3b-2b
5c=10a+b
5c=ab (cu bara deasupra)
c=1, 5*1=5, deci fals
c=2, ab=10, abc=102
c=3,ab=15,, abc=153
c=4, ab=20, abc=204
c=5, ab=25, abc=255
c=6, ab=30,, abc=306
c=7, ab=35, abc=357
c=8, ab=40, abc=408
c=9, ab=45, abc=459

S= Suma numerelor de sus=2244