Question

3. Ifx = 8, how much more wallpaper will you need for the living room than for the family room?(2 points each)a) What is the area of the living room when x = 8?Note: You will need tosubtract the area of theliving room from thefamily room.b) What is the area of the family room when x = 8?1c) Subtract the two areas to find how much more square feet the living room will require.

Answer 1

Question 4.

From the answers in part 1 and part 2, we have:

• Equation for the wallpaper of family room:

$y=21x^2-21$

• Equation for the wallpaper of the living room:

$y=16x^2$

Let's solve for the following:

• (a) Area of the living room when x = 8

Substitute 8 for x in the second equation which represents the area of the living room and evaluate:

$\begin{gathered} y=16x^2 \\ \\ y=16(8)^2 \\ \\ y=16(64) \\ \\ y=1024ft^2^{} \end{gathered}$

When x = 8, the area of the living room is 1024 square feet.

• (b). Area of the family room when x = 8.

Substitute 8 for x in the first equation which represents area of the familiy room and evaluate

$\begin{gathered} y=21x^2-21 \\ \\ y=21(8)^2-21 \\ \\ y=21(64)-21 \\ \\ y=1344-21 \\ \\ y=1323ft^2 \end{gathered}$

When x = 8, the area of the family room is 1323 square feet.

• (c). Let's determine how much more square feet the living room will require.

Area of family room - area of living room = 1323 square feet - 1024 square feet = 299 square feet.

Therefore, you will need 299 more square feet of wallpaper for the living room than the family room