Question

escreva em forma decimal os aumentos sucessivos e informe o aumento final .
a) aumento sucessivo de 14% e 20%
b) desconto sucessivo de 20% e 20%
c) aumento sucessivo de 5% , 10% e 15%
d) descontos sucessivo de 10,5% , 5,7% e 2,8%.

Answer 1

a)

$Aumento~de~14\%~=~100\%+14\%~=~\frac{100}{100}+\frac{14}{100}~=~\frac{114}{100}~=~\boxed{1,14}\\\\\\Aumento~de~20\%~=~100\%+20\%~=~\frac{100}{100}+\frac{20}{100}~=~\frac{120}{100}~=~\boxed{1,20}\\\\\\\\Aumento~Final~=~(Aumento~de~14\%)\times(Aumento~de~20\%)\\\\Aumento~Final~=~1,14\times1,20\\\\Aumento~Final~=~\boxed{1,368}\\\\Aumento~Final~=~\frac{136,8}{100}~=~\frac{100}{100}+\frac{36,8}{100}~=~\boxed{Aumento~de~36,8\%}$

b)

$Desconto~de~20\%~=~100\%-20\%~=~\frac{100}{100}-\frac{20}{100}~=~\frac{80}{100}~=~\boxed{0,80}\\\\\\Desconto~Final~=~(Desconto~de~20\%)\times(Desconto~de~20\%)\\\\Desconto~Final~=~0,80\times0,80\\\\Desconto~Final~=~\boxed{0,64}\\\\Desconto~Final~=~\frac{64}{100}~=~\frac{100}{100}-\frac{36}{100}~=~\boxed{Desconto~de~36\%}$

c)

$Aumento~de~5\%~=~100\%+5\%~=~\frac{100}{100}+\frac{5}{100}~=~\frac{105}{100}~=~\boxed{1,05}\\\\\\Aumento~de~10\%~=~100\%+10\%~=~\frac{100}{100}+\frac{10}{100}~=~\frac{110}{100}~=~\boxed{1,10}\\\\\\Aumento~de~15\%~=~100\%+15\%~=~\frac{100}{100}+\frac{15}{100}~=~\frac{115}{100}~=~\boxed{1,15}$

$Aumento~Final~=~(Aumento~de~5\%)\times(Aumento~de~10\%)\times(Aumento~de~15\%)\\\\Aumento~Final~=~1,05\times1,10\times1,15\\\\Aumento~Final~=~\boxed{1,32825}\\\\Aumento~Final~=~\frac{132,825}{100}~=~\frac{100}{100}+\frac{32,825}{100}~=~\boxed{Aumento~de~32,825\%}$

d)

$Desconto~de~10,5\%~=~100\%-10,5\%~=~\frac{100}{100}-\frac{10,5}{100}~=~\frac{89,5}{100}~=~\boxed{0,895}\\\\\\Desconto~de~5,7\%~=~100\%-5,7\%~=~\frac{100}{100}-\frac{5,7}{100}~=~\frac{94,3}{100}~=~\boxed{0,943}\\\\\\Desconto~de~2,8\%~=~100\%-2,8\%~=~\frac{100}{100}-\frac{2,8}{100}~=~\frac{97,2}{100}~=~\boxed{0,972}$

$Desconto~Final~=~0,895\times0,943\times0,972\\\\Desconto~Final~=~\boxed{0,82035342}\\\\Desconto~Final~=~\frac{82,035342}{100}~=~\frac{100}{100}-\frac{17,964658}{100}~=~\boxed{Desconto~de~17,964658\%}$