Solve for x. Please help me.
2 answers:
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Answer:
Part A
The width of the garden is approximately 3.987 meters
Part B
Please find attached the drawing of the solution
Step-by-step explanation:
Part A
The given parameters are;
The dimensions of the backyard of the home = 25 m by 30 m
The width of the garden to be built in the yard = Uniform width
The shape of the grass left inside = Rectangular
The area of the grass at the center = The area of the garden
Let 'x' represent the width of the garden, we have;
The length of the rectangular grass area at the center, l = 30 - 2·x
The width of the rectangular area of grass at the center, w = 25 - 2·x
The area of the rectangular backyard, A = 30 m × 25 m = 750 m²
The area of the rectangular backyard, A = (The area of the garden) + (The area of the rectangle of grass inside)
The area of the rectangle of grass, GA = (30 - 2·x)·(25 - 2·x) = The area of the garden
The area of the rectangular backyard, A = 750 = (30 - 2·x)·(25 - 2·x) + (30 - 2·x)·(25 - 2·x) = 2 × (30 - 2·x)·(25 - 2·x) = 8·x² - 220·x + 1,500
∴ 750 = 8·x² - 220·x + 1,500
8·x² - 220·x + 1,500 - 750 = 0
8·x² - 220·x + 750 = 0
x = (220 ± √(220² - 4 × 8 × 750))/(2 × 8)
x ≈ 23.513, or x = 3.987
When x = 25.513, the width of the rectangle of grass inside, w = 25 - 2 × 23.513 = -22.026, which is not a natural (physically possible)
Therefore, the possible width of the garden, x ≈ 3.987
Part B
The drawing of the solution created with MS Visio is attached
You have the right idea and you are close to the correct answer. However that's not what your teacher is looking for in terms of steps.
The starting inequality is
She starts off selling 8 buckets. Then she sells b more to get a total of b+8
This total must be 20 or larger which is why I set b+8 greater than or equal to 20
Solve for b by subtracting 8 from both sides
So she needs to sell at least 12 more buckets to reach her goal
If you graphed this on a number line, then you would draw a closed circle at 12. Then shade to the right of the close circle.
The starting inequality is
She starts off selling 8 buckets. Then she sells b more to get a total of b+8
This total must be 20 or larger which is why I set b+8 greater than or equal to 20
Solve for b by subtracting 8 from both sides
So she needs to sell at least 12 more buckets to reach her goal
If you graphed this on a number line, then you would draw a closed circle at 12. Then shade to the right of the close circle.