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Difficulty: Very hardRectangular Area Applications

An agricultural company is installing a weed-blocking fabric on the dirt floor of a rectangular greenhouse that is 120 feet120 \text{ feet} long and 45 feet45 \text{ feet} wide. Inside the greenhouse, there are three identical rectangular planting beds, each measuring 30 feet30 \text{ feet} by 12 feet12 \text{ feet}, which will not be covered by the fabric. The fabric is sold in rolls that cover 15 square yards15 \text{ square yards} each, and each roll costs $45\$45. Assuming partial rolls cannot be purchased and the company must buy whole rolls, what is the total cost of the fabric rolls needed to cover the designated floor area?

  1. A
    $990\$990
  2. B
    $4,320\$4,320
  3. $1,440\$1,440Answer
  4. D
    $12,960\$12,960

Answer

The total cost of the fabric rolls needed is $1,440\$1,440.
The correct total cost is found by determining the subtractive area in square feet (5,400−1,080=4,3205,400 - 1,080 = 4,320), converting that area to square yards by dividing by 99 (480 sq yd480 \text{ sq yd}), determining the number of 1515-square-yard rolls needed (3232), and multiplying by the price per roll ($45\$45).

Step-by-Step Solution

1
Calculate the total area of the greenhouse floor.
120 feet×45 feet=5,400 sq ft120 \text{ feet} \times 45 \text{ feet} = 5,400 \text{ sq ft}
This establishes the maximum possible area to be covered before accounting for the exclusions.
2
Calculate the total area of the three planting beds.
3×(30 feet×12 feet)=3×360 sq ft=1,080 sq ft3 \times (30 \text{ feet} \times 12 \text{ feet}) = 3 \times 360 \text{ sq ft} = 1,080 \text{ sq ft}
The planting beds are not getting covered, so their combined area must be subtracted.
3
Subtract the area of the planting beds from the total greenhouse area.
5,400 sq ft−1,080 sq ft=4,320 sq ft5,400 \text{ sq ft} - 1,080 \text{ sq ft} = 4,320 \text{ sq ft}
This provides the net area of the floor that requires the weed-blocking fabric.
4
Convert the net area from square feet to square yards.
4,320 sq ft÷9 sq ft/sq yd=480 sq yd4,320 \text{ sq ft} \div 9 \text{ sq ft/sq yd} = 480 \text{ sq yd}
The fabric is sold based on coverage in square yards, so the area units must match. There are 99 square feet in one square yard (3 ft×3 ft3 \text{ ft} \times 3 \text{ ft}).
5
Determine the number of rolls needed.
480 sq yd÷15 sq yd/roll=32 rolls480 \text{ sq yd} \div 15 \text{ sq yd/roll} = 32 \text{ rolls}
Dividing the total square yards by the coverage per roll gives the required number of rolls.
6
Calculate the total cost of the rolls.
32 rolls×$45/roll=$1,44032 \text{ rolls} \times \$45/\text{roll} = \$1,440
Multiplying the needed number of rolls by the price per roll provides the final cost.

Key Concept

Rectangular Area Applications
Estimated Time:2m 30s
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Topics

Rectangular Area Applications

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