Question

determinati numerele de forma abc in baza zece, stiind ca :
a)abc1 in baza 10+2abc in baza 10+abc4 in baza 10+3abc in baza 10=7975. b) abc in baza 10+6abc in baza 10+abc3 in baza 10=8955.

Answer 1

a)abc1 in baza 10+2abc in baza 10+abc4 in baza 10+3abc in baza 10=7975
1000a+100b+10c+1+2000+100a+10b+c+1000a+100b+10c+4+3000+100a+ 10b+c=7975
2200a+220b+22c=2970      : 22
100a+10b+c=135
c=5
b=3
a=1


b) abc in baza 10+6abc in baza 10+abc3 in baza 10=8955.
100a+10b+c+6000+100a+10b+c+1000a+100b+10c+3=8955
1200a+120b+12c=8955-6003
1200a+120b+12c=2952      :12
100a+10b+c=246
a=2
b=4
c=6