I'm not sure if this is exactly right because the wording of the problem is confusing.
a) Number of square feet of wallpaper for bedroom = 12x^2 - 21
b) Number of square feet of wallpaper for living room = 14x^2 - 42
c) Total amount of wallpaper needed = 26x^2 - 63
d) 107 more sq ft of wallpaper will be needed for the living room than bedroom.
Step-by-step explanation:
a) First find the area of each wall.
Length: 3x, Width: 3x, Height: x
(3x × x) + (3x × x) + (3x × x) + (3x × x) = 3x^2 + 3x^2 + 3x^2 + 3x^2 = 12x^2
12x^2 represents the amount of wallpaper needed, including the door. Find the area of the door and subtract it from this value.
3 × 7 = 21
12x^2 - 21 = Total sq ft of wallpaper needed for bedroom
b) First find the area of each wall.
Length: 4x, Width: 3x, Height: x
(4x × x) + (4x × x) + (3x × x) + (3x × x) = 4x^2 + 4x^2 + 3x^2 + 3x^2 = 14x^2
14x^2 represents the amount of wallpaper needed, including the door. Find the area of both doors and subtract it from this value.
3 × 7 = 21 × 2 = 42
42x^2 - 42 = Total sq ft of wallpaper needed for living room
c) Add the two expressions to find the total amount of wallpaper needed.
(12x^2 - 21) + (42x^2 - 42) = 26x^2 - 63
26x^2 - 63 = Total sq ft of wallpaper needed for both rooms
d) Plug x = 8 into the equations found in part a and b.
12(8)^2 - 21 = 747
14(8)^2 - 42 = 854
Subtract these answers to find the difference in amount.
854 - 747 = 107
The living room needs 107 sq ft more of wallpaper than the bedroom
