4.
[tex]\it 27^{17}=(3^3)^{17}=3^{3\cdot17}=3^{51}\\ \\ 9^{27}=(3^2)^{27}=3^{2\cdot27}=3^{54}\\ \\ 81^{13}=(3^4)^{13}=3^{4\cdot13}=3^{52}\\ \\ \\ 3^{54} > 3^{52} > 3^{51} \Rightarrow \dfrac{1}{3^{54}} < \dfrac{1}{3^{52}} < \dfrac{1}{3^{51}}|_{\cdot2,022} \Rightarrow \dfrac{2,022}{3^{54}} < \dfrac{2,022}{3^{52}} < \dfrac{2,022}{3^{51}}[/tex]
[tex]\it Deci:\ \ \dfrac{2,022}{9^{27}} < \dfrac{2,022}{81^{13}} < \dfrac{2,022}{27^{17}}[/tex]
5.
Notăm c = numărul copiilor ⇒ 24 - c = numărul adulților.
[tex]\it 7\cdot(24-c)+4,5c=125,5 \Rightarrow 168-7c+4,5c=125,5 \Rightarrow\\ \\ \Rightarrow 168-125,5=7c-4,5c \Rightarrow 42,5=2,5c|_{\cdot2} \Rightarrow 85=5c|_{:5} \Rightarrow c=17[/tex]
