Question

3. You have decided to wallpaper your rectangular bedroom. The dimensions are 12 feet 6 inches by 10 feet 6 inches by 8 feet 0 inches high. The room has two windows, each 4 feet by 3 feet and a door 7 feet by 3 feet. Determine how many rolls of wallpaper are needed to cover the walls, allowing 10% for waste and matching. Each roll of wallpaper is 30 inches wide and 30 feet long. How many rolls of wallpaper should be purchased? * OA. 4 rolls OB. 5 rolls OC. 6 rolls OD. 7 rolls OE. 8 rolls

Answer 1

Answer:

Correct answer is B. 5Rolls

Step-by-step explanation:

1. First you have to put all values in same unit of measurement,

• knowing that 1 foot=12 inches, we apply 3 rule:

12 inches is 1 feet

6 inches is 6/12 feet= 0,5 feet.

12 inches is 1 foot

30 inches is 30/12 feet=2,5feet.

2. Second,you have to calculate the total surface where you will wallpaper.

So you have to calculate the dimension of 2 different rectangles and substract the surfaces that you don't have to wallppaper (door and windows).

• Let's calculate the surface of the rectancles. Let's put all units in feets.

$Area rectangle 1 =10.5feet*8feet=84ft^{2} \\Area rectangle2=12.5feet*8feet=100ft^{2}\\Total Area of walls=(Area rectangle 1 *2) + (Area rectangle2*2)\\Total Area of walls=(84ft^{2} *2)+(100ft^{2})\\\\Total Area of walls=368ft^{2}$

3. Now we have to calculate the area to substract from the total area, since you will not wallpaper the door and windows:

$Windows=4feet*3feet*2=24ft^{2} \\Door=7feet*3feet=21ft^{2}$

4. Total area to wallpaper is Total surface of the room minus door and windows surface:

$wallpaperArea=368ft^{2} -45ft^{2}\\wallpaperArea=323ft^{2}$

5. Now you have to add 10% waste to the calculated surface:

$323ft^{2} +(323*0.10)=355.3ft^{2}$

6. So, you have the real area that will wallpaper considering 10% waste, it is 326.23 square feet. To calculate how many rolls you will need, you have to calculate the surface that each roll covers and then divide total surface by roll surface.

$Roll surface=2,5feet*30feet=75feet^{2}$

$Rolls needed=355.3ft^{2}/75ft^{2}=4.73$

7. As the number of rolls is not integer you have to round, then the answer is you will need 5 rolls of wallpaper.

Answer 2

Answer:

B. 5 rolls

Step-by-step explanation:

The areas of the room, not including the ceiling, are discriminated as follows:

Longer walls: $(12.5\times8)\times2=200ft^2$ (6 inches equals one foot)

Shorter walls: $(10.5\times8)\times2 = 168ft ^ 2$ (6 inches equals one foot)

Window area: $(4\times3)\times2 = 24ft ^ 2$

Door area: $(7\times3) = 21ft ^ 2$

Area that will be effectively covered:

Total area to wallpaper: $200 + 168 -24 -21 = 323ft ^ 2$

Amount of paper needed: $323\times1.1 = 355.3ft ^ 2$

$30in = 24in + 6in = 2ft + 0.5ft = 2.5ft.$ That is, the area of ​​a roll of paper is $2.5\times30 = 75ft ^ 2$

Number of rolls needed:

$\frac{355.3}{75} = 4.73$ rolls