Răspuns:
[tex]\boldsymbol{ \red{671 }}[/tex]
Explicație pas cu pas:
[tex]16,(6) \% = \dfrac{166 - 16}{9} \cdot \dfrac{1}{100} = \dfrac{150}{9} \cdot \dfrac{1}{100} = \dfrac{1}{6} \\[/tex]
[tex]20 \% = \dfrac{20}{100} = \dfrac{1}{5} \\[/tex]
Notăm cu a, b, c, d numărul de hectare lucrate zilnic
[tex]20\% \ din \ a = 16,(6)\% \ din \ b \Rightarrow \dfrac{1}{5}\cdot a = \dfrac{1}{6}\cdot b \Rightarrow b = \dfrac{6a}{5} \\[/tex]
[tex]\dfrac{1}{5}\cdot b = \dfrac{1}{6}\cdot c \Rightarrow \dfrac{1}{5} \cdot\dfrac{6a}{5} = \dfrac{c}{6} \Rightarrow c = \dfrac{36a}{25}\\[/tex]
[tex]\dfrac{1}{5}\cdot c = \dfrac{1}{6}\cdot d \Rightarrow \dfrac{1}{5} \cdot\dfrac{36a}{25} = \dfrac{d}{6} \Rightarrow d = \dfrac{216a}{125}\\[/tex]
[tex]d - a = 91 \Rightarrow \dfrac{216a}{125} - a = 91 \Rightarrow \dfrac{91a}{125} = 91 \Rightarrow \bf a = 125\\[/tex]
[tex]b = \dfrac{6 \cdot 125 }{5} = \bf 150[/tex]
[tex]c = \dfrac{36 \cdot 125}{25} = \bf 180[/tex]
[tex]d = 125 + 91 = \bf 216[/tex]
Total:
[tex]125+150+180+216 = \bf 671 \ ha[/tex]
