Resposta:
a = R$ 1.600,00
b = R$ 4.000,00
c = R$ 800,00
Explicação passo-a-passo:
Sejam a, b e c as partes.
[tex]a~+~b~+~c~=~6400~e~\frac{a}{\frac{1}{5} }~=\frac{b}{\frac{1}{2} } ~=\frac{c}{\frac{1}{10}}\\\\\frac{a+b+c}{\frac{1}{5}+\frac{1}{2}+\frac{1}{10} } ={\frac{1}{5} } \\\\\frac{6400}{\frac{2+5+1}{10} } =\frac{a}{\frac{1}{5} } \\\\\frac{6400}{\frac{8}{10} }=\frac{a}{\frac{1}{5} }\\\\\frac{8a}{10}=\frac{6400}{5} \\\\40a=6400.10\\\\40a=64000\\\\a=\frac{64000}{40}\\\\a=R\$~1.600,00[/tex]
[tex]\frac{6400}{\frac{8}{10} }=\frac{b}{\frac{1}{2} } \\\\\frac{8b}{10}=\frac{6400}{2}\\\\16b=64000\\\\b=\frac{64000}{16} \\\\b=R\$~4.000,00\\\\c=6.400-1600-4000\\\\c= R\$~800,00[/tex]
