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Difficulty: MediumRectangular Area Applications

An event coordinator is installing a temporary dance floor in a rectangular banquet room measuring 60 feet60\text{ feet} long and 45 feet45\text{ feet} wide. A fixed rectangular dining section that measures 30 feet30\text{ feet} by 15 feet15\text{ feet} will remain uncovered. If the temporary flooring material costs $4\$4 per square yard, what is the total cost of the flooring?

  1. A
    $480\$480
  2. $1,000\$1,000Answer
  3. C
    $3,000\$3,000
  4. D
    $9,000\$9,000

Answer

The total cost of the flooring is $1,000\$1,000.
The correct answer is found by first calculating the net area to be covered in square feet (2,700−450=2,250 sq ft2,700 - 450 = 2,250\text{ sq ft}). Then, this area must be converted to square yards by dividing by 99 (since 1 square yard=9 square feet1\text{ square yard} = 9\text{ square feet}), resulting in 250 square yards250\text{ square yards}. Finally, multiplying by the rate of $4\$4 per square yard yields $1,000\$1,000.

Step-by-Step Solution

1
Calculate the total area of the banquet room.
60 feet×45 feet=2,700 square feet60\text{ feet} \times 45\text{ feet} = 2,700\text{ square feet}
To find the maximum possible floor space before accounting for the uncovered section.
2
Calculate the area of the fixed dining section.
30 feet×15 feet=450 square feet30\text{ feet} \times 15\text{ feet} = 450\text{ square feet}
To determine how much space will not receive the temporary flooring.
3
Subtract the uncovered area from the total room area.
2,700−450=2,250 square feet2,700 - 450 = 2,250\text{ square feet}
To find the net area that requires the temporary dance floor.
4
Convert the net area from square feet to square yards.
2,250÷9=250 square yards2,250 \div 9 = 250\text{ square yards}
Because 1 square yard=9 square feet1\text{ square yard} = 9\text{ square feet} (3 ft×3 ft3\text{ ft} \times 3\text{ ft}), and the material is priced per square yard.
5
Calculate the total cost.
250 sq yd×$4/sq yd=$1,000250\text{ sq yd} \times \$4/\text{sq yd} = \$1,000
To find the final expense by multiplying the total required square yards by the price per square yard.

Key Concept

Calculating net rectangular area and performing two-dimensional unit conversions.
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Topics

Rectangular Area Applications

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