Question

one third of a land is on maize, a fifth of the remainder is on potatoes and the rest which is 0.5 ha is on beans. how much of the land is on potatoes?

Answer 1

Answer: $1250\ m^2$

Step-by-step explanation:

Let x= Total land.

Then for Maize = $\dfrac{x}{3}$    

For Potatoes = $\dfrac15(x-\dfrac {x}{3})=\dfrac15(\dfrac{2x}{3})=\dfrac{2}{15}x$

For beans = $x- (\dfrac{x}{3}+\dfrac{2}{15}x)=0.5 \ ha$

$\Rightarrow\ x- (\dfrac{5x+2x}{15})=0.5 \ ha\\\\\Rightarrow\ x- (\dfrac{7x}{15})=0.5 \ ha\\\\\Rightarrow\ \dfrac{15x-7x}{15}=0.5 \ ha\\\\\Rightarrow\ \dfrac{8x}{15}=0.5 \ ha\\\\\Rightarrow\ x=0.5\times\dfrac{15}{8} \ ha\\\\\Rightarrow\ x=0.9375 \ ha$

1 ha = 10000.00 m²

0.9375 ha = 9375 m²

Land for potatoes = $\dfrac{2}{15}(9375) =1250\ m^2$

Hence, $1250\ m^2$ of the land is on potatoes.