Answer:
Let's denote the width of the border as
�
x feet. Since the border goes around the outside of the flower bed, it would increase both the length and the width of the flower bed by
2
�
2x feet.
The new dimensions of the flower bed with the border will be:
Length:
10
+
2
�
10+2x feet
Width:
50
+
2
�
50+2x feet
The area of the flower bed with the border is given by the product of its length and width:
(
10
+
2
�
)
(
50
+
2
�
)
(10+2x)(50+2x)
According to the problem, the area covered by the pine bark is 396 square feet. So, we can set up the equation:
(
10
+
2
�
)
(
50
+
2
�
)
=
396
(10+2x)(50+2x)=396
Now, we can solve for
�
x:
500
+
20
�
+
2
�
2
=
396
500+20x+2x
2
=396
2
�
2
+
20
�
+
500
−
396
=
0
2x
2
+20x+500−396=0
2
�
2
+
20
�
+
104
=
0
2x
2
+20x+104=0
Divide the equation by 2:
�
2
+
10
�
+
52
=
0
x
2
+10x+52=0
Unfortunately, this quadratic equation doesn't have real solutions, as its discriminant (
�
2
−
4
�
�
b
2
−4ac) is negative. This indicates that the problem might not have a valid solution or there might be a mistake in the problem statement.
Explanation: