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

Correct answer is B. 5Rolls

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

B. 5 rolls

Explanation:

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

Longer walls:
`(12.5*8)*2=200ft^2` (6 inches equals one foot)

Shorter walls:
`(10.5*8)*2 = 168ft ^ 2` (6 inches equals one foot)

Window area:
`(4*3)*2 = 24ft ^ 2`

Door area:
`(7*3) = 21ft ^ 2`

Area that will be effectively covered:

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

Amount of paper needed:
`323*1.1 = 355.3ft ^ 2`

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

Number of rolls needed:

`(355.3)/(75) = 4.73` rolls