Question

Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to

paint the room and put in new flooring. The room is rectangular, with dimensions of (160 feet (length) by \(13\frac(1)
(210) feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows.
Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not
Including the cost of labor or other related materials. She was given the following information by the local flooring store
where she is purchasing the carpet.
She is required to purchase a plece of carpet which includes a 3-inch overlap on all sides. Labor and material costs
will relate to the area of this plece.
The labor costs are $23 per hour, per person.
A two-person carpet crew can lay 50 square feet of carpet each hour.
The crew that will complete the job at Charlotte's house will be a four-person crew.
There is an additional $75 fee to cover the cost of equipment, materials, and supplies.
What are the dimensions of the plece of carpet that Charlotte must purchase? Note: Express your answer as a decimal
number and do not round.

Answer 1

The dimensions of the piece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95

Explanation:

To determine the dimensions of the piece of carpet that Charlotte must purchase, we need to add the overlap to the length and width of the room.

The overlap is 3 inches, which is 0.25 feet (since there are 12 inches in a foot and 3/12 = 0.25).

So the length of the piece of carpet needed is 160.5 feet (160 + 0.25 + 0.25), and the width is 13.5 feet (13.25 + 0.25 + 0.25).

To find the area of the piece of carpet needed, we multiply the length by the width:

160.5 feet x 13.5 feet = 2166.75 square feet

Now we need to add the extra area needed for the overlap, which is:

0.25 feet x 0.25 feet x 4 (since there are 4 sides) = 0.25 square feet

So the total area of the piece of carpet needed is:

2166.75 square feet + 0.25 square feet = 2167 square feet

To determine the labor and material costs, we need to find the area of the plece (piece) of carpet, including the overlap.

The labor costs are $23 per hour, per person, and the crew can lay 50 square feet of carpet each hour. So the total labor cost will be:

4 people x $23 per hour per person = $92 per hour

To determine how many hours it will take to lay the carpet, we divide the total area of the plece by the rate at which the crew can lay carpet:

2167 square feet ÷ (4 people x 50 square feet per hour) = 10.835 hours

We will need to round up to the nearest whole number since the crew cannot work for a fraction of an hour. So it will take 11 hours to lay the carpet.

The cost of materials will be:

2167 square feet x $1.85 per square foot = $4001.95

The cost of labor and materials will be:

11 hours x $92 per hour = $1012

$1012 + $4001.95 + $75 equipment/materials/supplies fee = $5088.95

Therefore, the dimensions of the plece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95.