Question Number 10104 by konen last updated on 23/Jan/17
$$\frac{\mathrm{a}}{\mathrm{2}}=\frac{\mathrm{b}}{\mathrm{5}}\:,\sqrt{\mathrm{5a}}\:+\sqrt{\mathrm{2b}}\:=\mathrm{16} \\ $$$$\Rightarrow\frac{\mathrm{5a}}{\mathrm{2}}+\mathrm{b}=\overset{} {?} \\ $$
Answered by arge last updated on 23/Jan/17
$$\mathrm{5}{a}=\mathrm{2}{b},\sqrt{\mathrm{2}{b}}\:+\sqrt{\mathrm{2}{b}}\:=\mathrm{16} \\ $$$$\mathrm{2}\sqrt{\mathrm{2}{b}}\:=\mathrm{16} \\ $$$$\sqrt{\mathrm{2}{b}}\:=\mathrm{8} \\ $$$$\mathrm{2}{b}=\mathrm{64} \\ $$$${b}=\mathrm{32} \\ $$$$ \\ $$$$\mathrm{5}{a}=\mathrm{64} \\ $$$${a}=\frac{\mathrm{64}}{\mathrm{5}} \\ $$$$ \\ $$$$\frac{\mathrm{5}{a}}{\mathrm{2}}+{b}=\mathrm{32}+\mathrm{32}=\mathrm{64}\ast\ast\ast{RTA} \\ $$$$ \\ $$$$ \\ $$