A community garden allocates its total area among three crops: vegetables, herbs, and flow… — ACT

A community garden allocates its total area among three crops: vegetables, herbs, and flowers. Exactly $\frac{3}{8}$ of the total area is dedicated to vegetables, and $40\%$ of the remaining area is planted with herbs. If the remaining flower section covers $270$ square feet, what is the total area, in square feet, of the community garden?

A
$432$
B
$450$
$720$ Cevap
D
$1,080$
E
$1,200$

Cevap

The total area of the community garden is

720

square feet.

The correct answer is

720

square feet. Vegetables take

\frac{3}{8}

of the total area, leaving

\frac{5}{8}

. Herbs take

40\%

\frac{5}{8}

, which equals

\frac{2}{5} \times \frac{5}{8} = \frac{2}{8}

of the total. Subtracting the herb portion from the remaining portion leaves

\frac{5}{8} - \frac{2}{8} = \frac{3}{8}

of the total for flowers. Solving

\frac{3}{8} T = 270

gives

T = 720

square feet.

Adım Adım Çözüm

Calculate the remaining fractional area after allocating space for vegetables.

Since vegetables occupy

\frac{3}{8}

of the garden,

1 - \frac{3}{8} = \frac{5}{8}

of the total area remains.

The total area represents

1

whole, so subtracting the vegetable fraction gives the remaining fraction.

Determine the fractional area allocated to herbs.

Herbs take

40\%

of the remaining

\frac{5}{8}

. Converting

40\%

to a fraction gives

\frac{2}{5}

. Calculating

\frac{2}{5} \times \frac{5}{8} = \frac{2}{8} = \frac{1}{4}

of the total garden area.

Multiplying the percentage by the remaining fraction yields the portion of the whole garden used for herbs.

Find the fractional area remaining for flowers.

Subtract the herb fraction from the remaining area after vegetables:

\frac{5}{8} - \frac{2}{8} = \frac{3}{8}

of the total area.

The flower section represents whatever area is left after both vegetables and herbs are accounted for.

Set up an equation to solve for the total garden area

T

\frac{3}{8} T = 270 \implies T = 270 \times \frac{8}{3} = 720

square feet.

Dividing the actual area of flowers by its fractional share gives the total garden area.

Anahtar Kavram

Multi-step word problems involving sequential fractions and percentages of a remaining amount.

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