Examkin

Soru

Zorluk: OrtaRectangular Area Applications

A homeowner is planning to install new carpet in a rectangular living room that measures 18 feet18\text{ feet} long by 15 feet15\text{ feet} wide. Inside the room, there is a built-in rectangular closet measuring 9 feet9\text{ feet} long by 3 feet3\text{ feet} wide that will not be carpeted. If the selected carpet costs $20\$20 per square yard, what is the total cost of the carpet needed for the room?

  1. A
    $1,620
  2. B
    $440
  3. $540Cevap
  4. D
    $4,860

Cevap

$540
The correct answer accurately calculates the net area in square feet (270−27=243 sq ft270 - 27 = 243\text{ sq ft}), converts it to square yards by dividing by 9 (27 sq yd27\text{ sq yd}), and then multiplies by the rate of $20\$20 per square yard to find the total cost of $540\$540.

Adım Adım Çözüm

1
Calculate the total area of the living room.
18×15=270 sq ft18 \times 15 = 270\text{ sq ft}
You must first determine the total floor space before accounting for the uncarpeted closet area.
2
Calculate the area of the uncarpeted closet.
9×3=27 sq ft9 \times 3 = 27\text{ sq ft}
The area of the closet needs to be identified so it can be excluded from the total carpet cost.
3
Subtract the closet area from the total room area.
270−27=243 sq ft270 - 27 = 243\text{ sq ft}
This provides the net floor area that requires carpeting.
4
Convert the net area from square feet to square yards.
243÷9=27 sq yd243 \div 9 = 27\text{ sq yd}
The carpet is priced per square yard, and there are 9 square feet9\text{ square feet} in 1 square yard1\text{ square yard} (3 ft×3 ft3\text{ ft} \times 3\text{ ft}).
5
Calculate the total cost by multiplying the net area in square yards by the cost per square yard.
27×20=$54027 \times 20 = \$540
Multiplying the required amount of carpet by its unit price gives the final total cost.

Anahtar Kavram

Calculating subtractive areas in applied contexts and converting between square units.
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Rectangular Area Applications

Bu konudan daha fazla soru