RÄspuns :
1. a +( n -3) +(n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)= 185 I 2. m/2 = p/5
a+ 7n = 185 a+ 7n = 7Ā·26 + 3 = 7Ā·25 + 10 = 7Ā·24 + 17 (m-4)Ā·4 = p-4
variante: ana = 3 ani , piticii: 23,24,25,26,27,28,29 4m-16 = p-4 p=4m-12
" " " " " " " " " " """10 " " " " 22,23,24,25,26,27,28 5m/2 = 4m-12
" ' ' ' ' '' ' '' ' ' ' ' ' ' 17' ' ' ' ' ' ''''21,22,23,24,25,26,27 3m = 24 m = 8 p = 20
3. 2a +3b+4c = 32 deoarece 2a,4c si 32 = numere pare ā 3b= nr. parāb =nr. par
ptr. b = 2 ā 2a +4c = 26 a+2c =13 aā{1,3,5,7,9,11} cā{6,5,4,3,2,1}
ptr. b= 4 ā 2a+4c = 20 a+2c = 10 aā(0,2,4,6,8,10} cā{5,4,3,2,1.0}
ptr.b = 6 ā 2a+4c =14 a+2c = 7 aā{1,3,5,7} cā{3,2,1,0}
ptr. b = 8 ā 2a +4c = 8 a+2c = 4 aā{0,2,4} cā{2,1,0}
ptr. b = 10 ā 2a+4c = 2 c = 0 a = 1
4. a+b+c = 240 a- n = 25 b-n = 56 c-n =120 a = n+25 b = n+56 c= n+120
3n + 201 = 240 3n =39 n = 13 a = 38 b= 69 c = 133 doar a = divizibil cu 2
a+ 7n = 185 a+ 7n = 7Ā·26 + 3 = 7Ā·25 + 10 = 7Ā·24 + 17 (m-4)Ā·4 = p-4
variante: ana = 3 ani , piticii: 23,24,25,26,27,28,29 4m-16 = p-4 p=4m-12
" " " " " " " " " " """10 " " " " 22,23,24,25,26,27,28 5m/2 = 4m-12
" ' ' ' ' '' ' '' ' ' ' ' ' ' 17' ' ' ' ' ' ''''21,22,23,24,25,26,27 3m = 24 m = 8 p = 20
3. 2a +3b+4c = 32 deoarece 2a,4c si 32 = numere pare ā 3b= nr. parāb =nr. par
ptr. b = 2 ā 2a +4c = 26 a+2c =13 aā{1,3,5,7,9,11} cā{6,5,4,3,2,1}
ptr. b= 4 ā 2a+4c = 20 a+2c = 10 aā(0,2,4,6,8,10} cā{5,4,3,2,1.0}
ptr.b = 6 ā 2a+4c =14 a+2c = 7 aā{1,3,5,7} cā{3,2,1,0}
ptr. b = 8 ā 2a +4c = 8 a+2c = 4 aā{0,2,4} cā{2,1,0}
ptr. b = 10 ā 2a+4c = 2 c = 0 a = 1
4. a+b+c = 240 a- n = 25 b-n = 56 c-n =120 a = n+25 b = n+56 c= n+120
3n + 201 = 240 3n =39 n = 13 a = 38 b= 69 c = 133 doar a = divizibil cu 2
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