Question

aflati suma tuturor nr naturale de 2 cifre impartite la 7 dau rastul 3

Answer 1

D:7=C rest 3
D=7×C+3

Daca C=0
D=7×0+3=0+3=3
Dar 3 nu are 2 cifre

Daca C=1
D=7×1+3=7+3=10 are 2 cifre


Daca C=2
D=7×2+3=14+3=17 are 2 cifre


Daca C=3
D=7×3+3=21+3=24 are 2 cifre


Daca C=4
D=7×4+3=28+3=31 are 2 cifre


Daca C=5
D=7×5+3=35+3=38 are 2 cifre


Daca C=6
D=7×6+3=42+3=45 are 2 cifre


Daca C=7
D=7×7+3=49+3=52 are 2 cifre


Daca C=8
D=7×8+3=56+3=59 are 2 cifre


Daca C=9
D=7×9+3=63+3=66 are 2 cifre


Daca C=10
D=7×10+3=70+3=73 are 2 cifre


Daca C=11
D=7×11+3=77+3=80 are 2 cifre


Daca C=12
D=7×12+3=84+3=87 are 2 cifre


Daca C=13
D=7×13+3=91+3=94 are 2 cifre

Daca C=14
D=7×14+3=98+3=101 nu are 2 cifre

Pentru C>13 nu avem solutii

Numerele sunt:
10;17;24;31;38;45;52;59;66;73;80;87;94

Suma lor este:
10+17+24+31+38+45+52+59+66+73+80+87+94=
=(7×1+3)+(7×2+3)+(7×3+3)+(7×4+3)+(7×5+3)+(7×4+3)+(7×5+3)+(7×6+3)+(7×7+3)+(7×8+3)+(7×9+3)+(7×10+3)+(7×11+3)+(7×12+3)+(7×13+3)=
=3×13+7(1+2+3+4+...+13)=
=3×13+7(13×14:2)=
=3×13+7×13×7=
=13(3+7×7)=
=13(3+49)=
=13×52=
= 676