Answer: [tex]1250\ m^2[/tex]
Step-by-step explanation:
Let x= Total land.
Then for Maize = [tex]\dfrac{x}{3}[/tex]
For Potatoes = [tex]\dfrac15(x-\dfrac {x}{3})=\dfrac15(\dfrac{2x}{3})=\dfrac{2}{15}x[/tex]
For beans = [tex]x- (\dfrac{x}{3}+\dfrac{2}{15}x)=0.5 \ ha[/tex]
[tex]\Rightarrow\ x- (\dfrac{5x+2x}{15})=0.5 \ ha\\\\\Rightarrow\ x- (\dfrac{7x}{15})=0.5 \ ha\\\\\Rightarrow\ \dfrac{15x-7x}{15}=0.5 \ ha\\\\\Rightarrow\ \dfrac{8x}{15}=0.5 \ ha\\\\\Rightarrow\ x=0.5\times\dfrac{15}{8} \ ha\\\\\Rightarrow\ x=0.9375 \ ha[/tex]
1 ha = 10000.00 m²
0.9375 ha = 9375 m²
Land for potatoes = [tex]\dfrac{2}{15}(9375) =1250\ m^2[/tex]
Hence, [tex]1250\ m^2[/tex] of the land is on potatoes.
