Question

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Answer 1

 

$\displaystyle\bf\\1)~~5\%~din~400=5\%\times400=\frac{5}{100}\times400=5\times4=20\\\\2)~~80\%~din~120=80\%\times120=\frac{80}{100}\times120=80\times1,\!2=96~Lei\\\\3)~~600\times(1+30\%)=600\times\frac{130}{100}=6\times130=780~Lei\\\\4)~~10\%\cdot x=70\\\\\frac{10}{100}\cdot x=70\\\\x=70:\frac{10}{100}=70\cdot\frac{100}{10}=70\cdot10=700\\\\5)~~8\%\times m=32~Kg\\\\\frac{8}{100}\times m=32\\\\ m=32:\frac{8}{100}=32\times\frac{100}{8}=4\times100=400~Kg$

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$\displaystyle\bf\\6)~~p\%\times24=6\implies p\%=\frac{6}{24}=\frac{1}{4}=0,\!25=25\%\\\\7)~~5\%~din40\%~din~6000=5\%\times\left(40\%\times6000\right)=\\\\=5\%\times\left(\frac{40}{100} \times6000\right)=5\%\times\left(40 \times60\right)=\\\\=5\%\times2400=\frac{5}{100}\times2400=5\times24=120\\\\8)~~900\times(1-20\%)=900\times80\%=900\times\frac{80}{100}=9\times80=720~Lei\\\\9)~~80\%~din~a=1040\\\\\frac{80}{100}\times a=1040\\\\a=1040:\frac{80}{100}=1040\times\frac{100}{80}=13\times100=1300$

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$\displaystyle\bf\\10)~~a\times(1+15\%)=3680\\\\a\times\frac{115}{100}=3680\\\\a=3680:\frac{115}{100}=3680\times\frac{100}{115}=32\times100=3200~Lei\\\\11)~~p\%\times480=360\implies p\%=\frac{360}{480}=\frac{3}{4}=0,\!75=75\%\\\\12)~~p\%=\frac{28-25}{25}=\frac{3}{25}=\frac{12}{100}=12\%\\\\13)~~75\%~din~64\%~din~50=75\%\times\left(64\%\times50\right)=\\\\=75\%\times\left(\frac{64}{100} \times50\right)=75\%\times\frac{64}{2}=75\%\times32=\\\\=\frac{75}{100}\times32=\frac{3}{4}\times32=3\times8=24$

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$\displaystyle\bf\\\\14)~~\left[18000\times(1+10\%)\right]\times(1+20\%)=\\\\=\left[18000\times\frac{110}{100}\right]\times(1+20\%)=\\\\=\left[180\times110\right]\times(1+20\%)=19800\times(1+20\%)=\\\\=19800\times\frac{120}{100}=198\times120=23760~Lei\\\\15)~~(1+15\%)\times a=690~Lei\\\\\frac{115}{100}\times~a=690\\\\ a=690:\frac{115}{100}=690\times\frac{100}{115}=6\times100=600~Lei\\\\16)~~p\%=\frac{400-36}{400}=\frac{364}{400}=\frac{91}{100}=91\%$

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$\displaystyle\bf\\17a)~~\left[y\times(1+20\%)\right]\times(1-20\%)=480~Lei\\\\\left[y\times\frac{120}{100}\right]\times\frac{80}{100}=480\\\\y\times\frac{120}{100}\times\frac{80}{100}=480\\\\y\times\frac{12}{10}\times\frac{8}{10}=480\\\\y\times\frac{6}{5}\times\frac{4}{5}=480\\\\y\times\frac{6\times4}{5\times5}=480\\\\y\times\frac{24}{25}=480\\\\y=489:\frac{24}{25}=480\times\frac{25}{24}=20\times25=500~Lei\\\\17b)~~p\%=\frac{500-480}{480}=\frac{20}{480}=\frac{1}{24}\approx0,04\approx4\%$