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A farmer uses 1/3 of his land to plant cassava, 2/5 of the remaining and to plant maize and the rest vegetables.if vegetables cover an area of 10acres,what is the total area of the farmers land.

Respuesta :

Cassava = 1/3 of his land

Remaining after planting Cassava = 1 - 1/3 = 2/3 of his land

Maize = 2/5 x 2/3 = 4/15 of his land

Vegetables = 2/3 - 4/15 = 2/5 of his land



If vegetables = 10 acres

2/5 of his land = 10 acres

1/5 of his land = 10 ÷ 2 = 5 acres

5/5 of his land = 5 x 5 = 25 acres

Answer: Total area 25 acres.
boffeemadrid

The total area of the land is required.

The total area of the farmer's land is 37.5 acres.

Let the total area of the land be [tex]x[/tex]

Remaining vegetables area is 10 acres.

Area used for cassava = [tex]\dfrac{1}{3}x[/tex]

Area used for maize

[tex]\dfrac{2}{5}(1-\dfrac{1}{3})x=\dfrac{4}{15}x[/tex]

Remaining vegetables

[tex]x-(\dfrac{1}{3}x+\dfrac{4}{15}x)=\dfrac{2}{5}x[/tex]

[tex]\dfrac{2}{5}x=10\\\Rightarrow x=\dfrac{10\times 5}{2}=25[/tex]

The total area of the farmer's land is 25 acres.

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