A community garden allocates space among three categories: vegetable beds, herb gardens, a… — ACT

A community garden allocates space among three categories: vegetable beds, herb gardens, and flower borders. Vegetable beds take up $\frac{3}{8}$ of the total area, herb gardens take up $0.25$ of the total area, and flower borders occupy the remaining 1,800 square feet. What is the total area, in square feet, of the community garden?

A
2,700
B
2,880
4,800Answer
D
675
E
7,200

Answer

4,800 square feet

To find the total area, first convert

0.25

\frac{2}{8}

. Summing the vegetable portion (

\frac{3}{8}

) and the herb portion (

\frac{2}{8}

) gives

\frac{5}{8}

of the garden. The flower section takes up the remaining

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

of the area. Setting

\frac{3}{8}

of the total area equal to 1,800 square feet and dividing 1,800 by

\frac{3}{8}

gives

1,800 \times \frac{8}{3} = 4,800

square feet.

Step-by-Step Solution

Convert the decimal portion to a fraction with a common denominator.

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

Converting all given portions into fractions with a common denominator allows direct addition.

Calculate the combined fraction for vegetable beds and herb gardens.

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

Adding the two known fractions identifies the combined portion of the garden accounted for by vegetables and herbs.

Find the fraction representing the flower borders.

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

Subtracting the combined fraction from the whole (1) yields the fractional part representing the remaining 1,800 square feet.

Solve for the total garden area.

\text{Total Area} = 1,800 \div \frac{3}{8} = 1,800 \times \frac{8}{3} = 4,800\text{ sq ft}

Dividing the part by its corresponding fractional portion calculates the whole quantity.

Key Concept

Combining fractions and decimals to solve part-to-whole problems

Estimated Time:1m 30s

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