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A farmer uses \(\frac{2}{5}\) of his land to grow cassava, \(\frac{1}{3}\) of th...


Question

A farmer uses \(\frac{2}{5}\) of his land to grow cassava, \(\frac{1}{3}\) of the remaining for yam and the rest for maize. Find the part of the land used for maize

Options

A) \(\frac{2}{15}\)

B) \(\frac{2}{5}\)

C) \(\frac{2}{3}\)

D) \(\frac{4}{5}\)

The correct answer is B.

Explanation:

Let x represent the entire farmland

then, \(\frac{2}{5}\)x + \(\frac{1}{3}\)[x - \(\frac{2}{3}x\)] + M = x

Where M represents the part of the farmland used for growing maize, continuing

\(\frac{2}{5}\)x + \(\frac{1}{3}\)x [1 - \(\frac{2}{3}x\)] + M = x

\(\frac{2}{5}x + \frac{1}{3}\)x [\(\frac{3}{5}\)] + M = x

\(\frac{2}{5}\)x + \(\frac{1x}{5}\) + M = x

\(\frac{3x}{5} + M = x\)

M = x - \(\frac{2}{5}\)x

= x[1 - \(\frac{3}{5}\)]

= x[\(\frac{2}{5}\)] = \(\frac{2x}{5}\)

Hence the part of the land used for growing maize is

\(\frac{2}{5}\)


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Dicussion (1)

  • Let x represent the entire farmland

    then, \(\frac{2}{5}\)x + \(\frac{1}{3}\)[x - \(\frac{2}{3}x\)] + M = x

    Where M represents the part of the farmland used for growing maize, continuing

    \(\frac{2}{5}\)x + \(\frac{1}{3}\)x [1 - \(\frac{2}{3}x\)] + M = x

    \(\frac{2}{5}x + \frac{1}{3}\)x [\(\frac{3}{5}\)] + M = x

    \(\frac{2}{5}\)x + \(\frac{1x}{5}\) + M = x

    \(\frac{3x}{5} + M = x\)

    M = x - \(\frac{2}{5}\)x

    = x[1 - \(\frac{3}{5}\)]

    = x[\(\frac{2}{5}\)] = \(\frac{2x}{5}\)

    Hence the part of the land used for growing maize is

    \(\frac{2}{5}\)

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