Răspuns:
1. notam caiete= a carti= b
2a + 3b= 50 3a+ 4b= 69 daca le scadem avem a+b= 19 lei
6a + 8b - 6a -9b =
6a + 9b- 6a - 8b= 150- 138 => b= 150- 138=> b= 12 lei (1 carte)
2a= 50 - 3 x12= 50-36 2a= 14=> a= 14:2 = 7 lei a= 7 lei ( 1 caiet)
2.
2x (1+2+3+...+50)= 7650 => 2x = 7650 : ( 1+2+3+...+50)
1+2+3+...+ 50= 50x51:2= 1275
2x= 7650 :1275 => 2x= 6 x= 6:2 = 3 x= 3
3. a+b+c= 1838 jucarii ( a, b, c - cele 3 zile)
c= 2a+54 c= b+75 2a+ 54= b+75 2a =b+75- 54= b+21
b= 2a- 21
a+ 2a- 21 + 2a +54= 1838
5a = 1838+ 21 -54 = 1805 a= 1805 :5 = 361 a= 361 jucarii in prima zi
b= 2x361 - 21 = 701 b= 701 jucarii a doua zi
c= 2 x361+ 54= 776 c= 776 jucarii a treia zi
4. [tex]3^{n} * 5^{n}[/tex] ( 3+ [tex]5^{3}[/tex] - 2 * [tex]3^{2}[/tex]) = [tex]3^{n} * 5^{n}[/tex] ( 3 + 125 - 18) = [tex]3^{n} * 5^{n}[/tex] *110
ultima cifra va fi 0 ( exemplu 3 * 5 *110= 1650 , 9 *25* 110=24750)
5. [tex]4^{112}[/tex] ( 1 + 4 + [tex]4^{2}[/tex] + [tex]4^{3}[/tex]) = [tex]4^{112}[/tex] ( 5+16 + 64) = [tex]4^{112}[/tex] * 75 : 5 se imparte la 5 exact
6. [ ( b+ 1) x 2 + 3]x4 = p p:2= 10 p=20
[ ( b+ 1) x 2 + 3]x4= 20
[ ( b+ 1) x 2 + 3] = 20 :4 = 5
(b+1)x 2 = 5-3 = 2
(b+1) x2= 2 b+ 1= 2:2 = 1 b+1= 1 => b=0 0 briose
