What will it cost to carpet a room 10 feet wide and 12 feet long if carpet costs $12.51 per square yard?
A. $166.80
B. $213.50
C. $186.23
D. $165.12
Answer (2)
Calculate the area of the room in square feet: A re a = 10 × 12 = 120 sq. ft.
Convert the area to square yards: A re a = 9 120 = 3 40 sq. yd.
Multiply the area in square yards by the cost per square yard to find the total cost: C os t = 3 40 × 12.51 = 166.8 .
The total cost to carpet the room is: $166.80 .
Explanation
Problem analysis We are given a room that is 10 feet wide and 12 feet long, and we want to carpet it. The carpet costs $12.51 per square yard. Our goal is to find the total cost of carpeting the room.
Calculate the area in square feet First, we need to find the area of the room in square feet. The area of a rectangle is given by the formula: A re a = w i d t h × l e n g t h In our case, the width is 10 feet and the length is 12 feet. So, the area in square feet is: A re a = 10 f t × 12 f t = 120 s q . f t
Convert area to square yards Next, we need to convert the area from square feet to square yards. Since 1 yard = 3 feet, 1 square yard = 9 square feet. To convert square feet to square yards, we divide by 9: A re a y a r d s = 9 A re a f ee t A re a y a r d s = 9 120 = 3 40 s q . y d
Calculate the total cost Now, we can calculate the total cost of the carpet. The carpet costs $12.51 per square yard, and we need 3 40 square yards. So, the total cost is: C os t = A re a y a r d s × p r i c e p er y a r d C os t = 3 40 × 12.51 C os t = 3 40 × 12.51 = 3 500.4 = 166.8
Final answer Therefore, the total cost to carpet the room is $166.80.
Examples
When planning home renovations, calculating the area of rooms and converting units like square feet to square yards is essential for accurate budgeting. For example, if you're tiling a bathroom or installing hardwood floors, knowing the area in square yards helps you determine the amount of material needed and the overall cost of the project. This ensures you purchase the correct quantity of materials and avoid overspending.
The total cost to carpet the room is calculated to be $166.80. This was determined by first finding the area of the room in square feet, then converting it to square yards, and finally multiplying the area by the cost per square yard of carpet. The correct answer is therefore option A: $166.80.
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