A rectangular community hall measures 60 \text{ feet} long and 45 \text{ feet} wide. A rec… — Armed Services Vocational Aptitude Battery (ASVAB)

A rectangular community hall measures $60 \text{ feet}$ long and $45 \text{ feet}$ wide. A rectangular stage measuring $15 \text{ feet}$ long and $12 \text{ feet}$ wide is located inside the hall and will not be carpeted. If commercial carpet costs $\$24$ per square yard, what is the total cost to carpet the remainder of the hall?

A
$1,248
$6,720Answer
C
$20,160
D
$60,480

Answer

The total cost to carpet the remainder of the hall is $6,720.

The correct approach requires finding the net area to be carpeted in square feet (

2,700 - 180 = 2,520

), converting it to square yards by dividing by 9 (

280 \text{ sq yd}

), and multiplying by the cost per square yard (

24) to reach the final cost of

6,720.

Step-by-Step Solution

Calculate the total area of the community hall.

60 \times 45 = 2,700 \text{ square feet}

To find the gross area before removing the uncarpeted section.

Calculate the area of the uncarpeted stage.

15 \times 12 = 180 \text{ square feet}

To determine the exact area that will not receive carpet.

Subtract the stage area from the total hall area.

2,700 - 180 = 2,520 \text{ square feet}

To find the net area that requires carpeting.

Convert the net area from square feet to square yards.

2,520 \div 9 = 280 \text{ square yards}

Because the carpet cost is given per square yard, and $1 \text{ square yard} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet}.

Calculate the total cost of the carpet.

280 \times 24 = \$6,720

To find the final price by multiplying the area in square yards by the cost per square yard.

Key Concept

Calculating the net area by subtracting a smaller rectangular region from a larger one, and converting between square units (

1 \text{ sq yd} = 9 \text{ sq ft}

) before calculating total cost.

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Step-by-Step Solution

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