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 16 feet (length) by 13 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 piece of carpet which includes a 3-inch overlap on all sides. Labor and material costs will relate to the area of this piece.
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.
questions:

1. What are the dimensions of the piece of carpet that Charlotte must purchase? Note: Express your answer as a decimal number and do not round.
length:____ feet width_____ feet
2. Recall that the area of a rectangle is found by multiplying the length and width of the rectangle. What is the area of the piece of carpet that Charlotte must purchase? Note: Express your answer as a decimal number and do not round.
______ square feet
3. How many hours should it take for the four-person crew to lay the flooring in Charlotte's bedroom? Note: Express your answer as a decimal number and round to the nearest one-hundredths place.
_____ hours
PLEASE HELP!!

Answer 1

To find the dimensions of the carpet, add the overlap to the length and width of the room. The area of the carpet is found by multiplying the length and width. Divide the area of the carpet by the rate at which a two-person crew can lay carpet to find the number of hours for a four-person crew.

Step-by-step explanation:

To find the dimensions of the piece of carpet Charlotte must purchase, we need to add the overlap to the length and width of the room. The overlap is 3 inches on all sides, which is equivalent to 0.25 feet. So the length of the carpet will be 16 + 2(0.25) and the width will be 13 + 2(0.25).

The area of the piece of carpet can be found by multiplying the length and width of the carpet. So the area of the carpet will be (16 + 2(0.25)) * (13 + 2(0.25)).

To calculate the number of hours it will take for the four-person crew to lay the flooring, we divide the area of the carpet by the rate at which a two-person crew can lay carpet. So the number of hours will be (16 + 2(0.25)) * (13 + 2(0.25)) / (50 * 2).

Answer 2

dimensions of the room------------------- >16*13
1 in---------------- >0.0833333 foot
3 in----------------- >x
x=3*.0833333=0.25 ft
Let
C-------------- > dimensions of the piece of carpet that Charlotte must purchase
C-------------- > (16+2*0.25)*(13+2*0.25)---------- > (16.50)*(13.50)=222.75 ft²

The answer a the question 1) is 16.50 feet X 13.50 feet

The answer a the question 2) is 222.75 ft²

3. How many hours should it take for the four-person crew to lay the flooring in Charlotte's bedroom?

if two-person carpet crew can lay 50 square feet of carpet---------- > 1 hour
four person carpet crew can lay 100 square feet of carpet---------- > 1 hour

therefore

if 100 ft² carpet----------------------- > 1 hour
222.75 ft² carpet--------------------- > x
x=222.75/100=2.2275 hours=2.23 hours

The answer is 2.23 hours