If the trend continued, in how many years would the median home value be $170,000? Show how obtained your answer using the linear equation you found in part c)

Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 86 feet.
Set up an equation for the perimeter involving only L, the length of the rectangle.
Solve this linear equation algebraically to find the length of the rectangle. Find the width as well.
Length___,width____
Using the same width from your answer or part b), find a new perimeter when the new length is five less than three times the width.
Explain the work in one or two sentences.

b. Length = L Ft.

Width = (L-3) Ft.
P = 2L + 2(L-3).

P = 2L + 2L - 6 = 86.
4L = 86 + 6 = 92
L = 23 Ft.
W = L - 3 = 32 - 3 = 29 Ft.

c. Width = 29 Ft.
Length = (3W-5) = (3*29 - 5 = 82 Ft.

P = 2L + 2W = 2*82 + 2*29 = 222 Ft.

b. Correction: W = L-3 = 23 - 3 = 20 Ft.

c. Width = 20 Ft.
Length = (3W-5) = 3*20 - 5 = 55 Ft.

P = 2L + 2W = 2*55 + 2*20 = 150 Ft.

To answer the first question regarding the trend of median home value, we need to use the linear equation obtained in part C. First, let's assume that the number of years is represented by "y", and the median home value is represented by "V".

The linear equation we found in part C is: V = 15000y + 120000

To find the number of years it will take for the median home value to be $170,000, we need to solve for "y" in the equation:

170000 = 15000y + 120000

To isolate "y", we can subtract 120,000 from both sides of the equation:

170000 - 120000 = 15000y

50000 = 15000y

Now, divide both sides of the equation by 15000:

50000 / 15000 = y

y = 3.33

Since "y" represents the number of years, we round it up to 4 years. Therefore, if the trend continues, the median home value will be $170,000 in approximately 4 years.

Moving on to the second question about the rectangle, let's set up an equation for the perimeter involving only the length (L) of the rectangle.

Given that the width (W) is three feet shorter than the length, we can represent the width as W = L - 3.

The perimeter of a rectangle is calculated by adding up all its sides:

Perimeter = 2 * (Length + Width)

Substituting the values, we can write the equation:

86 = 2 * (L + (L - 3))

Simplifying this equation, we get:

86 = 2 * (2L - 3)

To continue, let's distribute the 2:

86 = 4L - 6

Next, we isolate 4L by adding 6 to both sides of the equation:

86 + 6 = 4L

92 = 4L

Lastly, we divide by 4 to solve for L:

L = 92 / 4

L = 23

So, the length of the rectangle is 23 feet.

Since the width (W) is three feet shorter than the length, we can substitute the length into the equation we used earlier:

W = L - 3
W = 23 - 3
W = 20

Therefore, the width of the rectangle is 20 feet.

For the third question, if we use the same width from part B (which is 20 feet), and the new length is five less than three times the width, we can calculate the new perimeter.

New Length = 3W - 5
New Length = 3(20) - 5
New Length = 60 - 5
New Length = 55

To find the new perimeter, we can apply the same formula as before:

New Perimeter = 2 * (New Length + Width)
New Perimeter = 2 * (55 + 20)
New Perimeter = 2 * 75
New Perimeter = 150

Therefore, the new perimeter when the new length is five less than three times the width is 150 feet.

In summary, I explained how to determine the number of years it would take for the median home value to reach $170,000 using a linear equation. Additionally, I demonstrated how to set up an equation to find the length and width of a rectangle based on its perimeter. Finally, I explained how to calculate a new perimeter using a given length and width.