A landscape architect is designing a public park with a total area of 14,400\text{ square … — ACT

A landscape architect is designing a public park with a total area of $14,400\text{ square feet}$ . The plan allocates space for a lawn, flowerbeds, and paved walkways in the ratio $7 : 3 : 2$ , respectively. How many more square feet of area are dedicated to the lawn than to the flowerbeds?

A
3,600
4,800Answer
C
5,760
D
6,000
E
8,400

Answer

4,800 square feet

The sum of all ratio parts is

7 + 3 + 2 = 12

. Dividing the total park area of

14,400\text{ sq ft}

12

gives

1,200\text{ sq ft}

per ratio part. The lawn accounts for

7

parts (

8,400\text{ sq ft}

) and the flowerbeds account for

3

parts (

3,600\text{ sq ft}

). Subtracting the flowerbed area from the lawn area gives

8,400 - 3,600 = 4,800\text{ sq ft}

. Alternatively, taking the direct difference of

7 - 3 = 4

parts and multiplying by

1,200\text{ sq ft}

gives

4,800\text{ sq ft}

Step-by-Step Solution

Find the total number of equal ratio parts.

7 + 3 + 2 = 12\text{ parts}

The complete park area is divided into portions defined by the sum of all terms in the ratio.

Calculate the area corresponding to one ratio part.

\frac{14,400}{12} = 1,200\text{ square feet per part}

Dividing the total area by the total number of parts determines the size of a single unit part.

Determine the difference in ratio parts between the lawn and the flowerbeds.

7 - 3 = 4\text{ parts}

The lawn receives 7 parts and the flowerbeds receive 3 parts.

Multiply the difference in parts by the area per part.

4 \times 1,200 = 4,800\text{ square feet}

Multiplying the difference in ratio units by the unit area yields the total excess area of the lawn over the flowerbeds.

Key Concept

Solving multi-part ratio word problems using unit rate allocation per ratio part.

Estimated Time:1m 15s

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