At an urban hydroponic farm, a monthly harvest consists of three types of crops: leafy gre… — GMAT

At an urban hydroponic farm, a monthly harvest consists of three types of crops: leafy greens, herbs, and microgreens. Leafy greens account for $\frac{5}{8}$ of the total harvest by weight, and herbs account for $0.25$ of the total harvest by weight. If the yield of microgreens increases by $40\%$ in the following month while the yields of leafy greens and herbs remain constant, what fraction of the new total harvest by weight will be microgreens?

A
$\frac{7}{40}$
$\frac{1}{6}$ Cevap
C
$\frac{1}{5}$
D
$\frac{7}{22}$
E
$\frac{7}{32}$

Cevap

The fraction of the new total harvest that will be microgreens is

\frac{1}{6}

Initially, leafy greens and herbs account for

\frac{5}{8} + 0.25 = \frac{5}{8} + \frac{2}{8} = \frac{7}{8}

of the total harvest weight, leaving microgreens with

1 - \frac{7}{8} = \frac{1}{8}

of the total weight. When microgreens increase by

40\%

, their new yield becomes

\frac{1}{8} \times 1.40 = \frac{7}{40}

of the original total harvest. The total harvest weight increases to

\frac{7}{8} + \frac{7}{40} = \frac{35}{40} + \frac{7}{40} = \frac{42}{40}

. The fraction of microgreens in this new total harvest is

\frac{7/40}{42/40} = \frac{7}{42} = \frac{1}{6}

Adım Adım Çözüm

Convert all initial crop portions into consistent fractions to find the initial microgreens fraction.

Leafy greens =

\frac{5}{8}

. Herbs =

0.25 = \frac{1}{4} = \frac{2}{8}

. Microgreens fraction =

1 - \left(\frac{5}{8} + \frac{2}{8}\right) = 1 - \frac{7}{8} = \frac{1}{8}

The sum of all three crop fractions must equal

1

(the total harvest).

Calculate the updated relative weight of microgreens after a

40\%

increase.

New microgreens weight relative to original total =

\frac{1}{8} \times (1 + 0.40) = \frac{1}{8} \times \frac{7}{5} = \frac{7}{40}

Increasing a quantity by

40\%

is equivalent to multiplying by

1.40

\frac{7}{5}

Determine the new total harvest weight relative to the original harvest.

New total harvest = Leafy greens + Herbs + New microgreens =

\frac{5}{8} + \frac{2}{8} + \frac{7}{40} = \frac{35}{40} + \frac{7}{40} = \frac{42}{40} = \frac{21}{20}

Since the yields of leafy greens and herbs did not change, their combined relative weight remains

\frac{35}{40}

Compute the fraction of the new total harvest that consists of microgreens.

Fraction =

\frac{\frac{7}{40}}{\frac{42}{40}} = \frac{7}{42} = \frac{1}{6}

Dividing the new microgreens weight by the new total harvest weight gives the updated proportion.

Anahtar Kavram

Fractions, Decimals, and Percents Arithmetic

Tahmini Süre:1m 30s

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