Answer:
The length = 20
The width = 12
Explanation:
Let the Length of the garden be L and the Width W
Therefore the area of the garden = L*W
But we know that L = W + 8
Therefore the area of the garden can be expressed as W*(W + 8)
When the brackets are expanded this equals W^2 + 8W
The area of the recctangle which includes the path and garden will have a length of L + 8 (ie the length of the garden + 4 feet at the top and 4 feet at the bottom)
The width will be W + 8 (width of garden + 4 feet at the left and 4 feet at the right)
Therefore the area will be (W + 8)*(L +8)
Once again we know that L = W + 8
Therefore the area of the path/garden = (W +8)(W +8 +8)
=(W +8)(W +16)
=W^2 +24W + 128
We know that the path alone has an area of 320 square feet. Therefore if we subtract the area of the garden (W^2 + 8W) from the area of the path/garden the area left is the area of the path only
Therefore W^2 + 24W + 128 - (W^2 + 8W) = 320
W^2 + 24W + 128 - W^2 - 8W = 320
Simplify
16W + 128 = 320
Subtract 128 from both sides of the equation
16W = 192
divide both sides of the equation by 16
W = 12
As L = W + 8
L = 12 + 8 = 20
For direct variation:
y = kx
9 = 12k
k = 9/12 = 3/4
Please take a look at the image attached.
Let's present a solution for the generic case.
The equation will be of the form y=ax+b
If (7,3) is on it, then 3=7a+b
If (14,6) is on it, then 6=14a+b
Now we have a system we can solve.
3=7a+b => b = 3-7a
6=14a + 3-7a => 3 = 7a => a=3/7
b = 3-7*3/7 = 0
So y = (3/7)x is the equation.
Salary because it depends on how much the plant cost
