Question

11. Calculaţi suma numerelor naturale de două cifre care, prin împărțire la 5, dau restul 3.

Va rog ajutati-ma urgentt!!!!!!​

Answer 1

Răspuns: 999

Explicație pas cu pas:

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ab : 5 = c rest 3

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ab = 5 × cât + 3

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5 × 2 + 3 = 13

5 × 3 + 3 = 18

5 × 4 + 3 = 23

5 × 5 + 3 = 28

5 × 6 + 3 = 33

5 × 7 + 3 = 38

5 × 8 + 3 = 43

5 × 9 + 3 = 48

5 × 10 + 3 = 53

5 × 11 + 3 = 58

5 × 12 + 3 = 63

5 × 13 + 3 = 68

5 × 14 + 3 = 73

5 × 15 + 3 = 78

5 × 16 + 3 = 83

5 × 17 + 3 = 88

5 × 18 + 3 = 93

5 × 19 + 3 = 98

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Suma numerelor:

13+18+23+28+33+38+43+48+53+58+63+68+73+78+83+88+93+98=

= 31+51+71+91+111+131+151+171+191=

= 82+162+242+322+191 =

= 999

Answer 2

$\it n=\overline{ab}\ \ \ \ (*)\\ \\ n:5=c\ \ rest\ \ 3 \Rightarrow n=5c+3\ \stackrel{(*)}{\Longrightarrow}\ n\in\{13, 18,\ 23,\ ...,\ 98\}$

$\it S=\dfrac{(13+98)\cdot18}{2}=111\cdot9=999$