Helga owns a campground, and she has installed a rectangular swimming pool measuring 10m by 20m. She wants to put a wooden deck of uniform width around the pool.
A. Helga has budgeted $1920 to spend on the deck and knows that construction costs are $30/m^2. What is the widest that that the deck can be?
B. Helga decides that the deck she can build $1920 is not big enough, so she budgets $6000 for the deck. How wide can the deck be now?
pls help
A. To find the widest that the deck can be within the budget of $1920, we need to subtract the cost of the pool from the total budget and then divide that amount by the cost per square meter.
The area of the pool is given by the length multiplied by the width:
Area = length * width
Area = 10m * 20m
Area = 200m^2
Now we can find the cost of the pool:
Cost of the pool = Area * cost per square meter
Cost of the pool = 200m^2 * $30/m^2
Cost of the pool = $6000
To find the widest width for the deck, we subtract the cost of the pool from the budget:
Remaining budget = Total budget - Cost of the pool
Remaining budget = $1920 - $6000
Remaining budget = -$4080
Since the remaining budget is negative, it means there is not enough money to build the deck. Therefore, the deck cannot be constructed with the given budget.
B. Now, let's consider the increased budget of $6000. We can repeat the same calculations to find the new maximum width for the deck.
The remaining budget after deducting the cost of the pool:
Remaining budget = Total budget - Cost of the pool
Remaining budget = $6000 - $6000
Remaining budget = $0
Since the remaining budget is $0, it means all the budget has been used. We can calculate the maximum area we can afford:
Maximum area = Remaining budget / cost per square meter
Maximum area = $0 / $30/m^2
Maximum area = 0m^2
This means that with the budget of $6000, we cannot afford to build any additional deck around the pool.
In conclusion, with the given budgets, it is not possible to construct the deck around the pool.
A. To find the widest that the deck can be, we need to determine the maximum width given the budget and construction costs.
1. Calculate the area of the pool:
Area = length × width
Area = 10m × 20m
Area = 200m^2
2. Determine the cost of the pool deck:
Construction cost = cost per m^2 × area
Construction cost = $30/m^2 × 200m^2
Construction cost = $6000
3. Calculate the amount available for the deck after deducting pool construction cost from the budget:
Available budget = budget - construction cost
Available budget = $1920 - $6000
Available budget = -$4080
Since the available budget is negative, it means that Helga cannot afford to build a deck with the given budget. Therefore, the widest the deck can be is zero meters.
B. If Helga decides to budget $6000 for the deck, we need to calculate the maximum width given the new budget.
1. Calculate the amount available for the deck now:
Available budget = new budget - construction cost
Available budget = $6000 - $6000
Available budget = $0
2. Calculate the maximum area the deck can have:
Maximum area = available budget / cost per m^2
Maximum area = $0 / $30/m^2
Maximum area = 0m^2
Since the available budget is zero, it means that Helga cannot afford to build a deck with the new budget. Therefore, the widest the deck can be is zero meters.
Sure, I can help you with that!
To find the widest that the deck can be, we need to consider the area and the cost involved.
A. Helga's budget is $1920, and the construction cost is $30/m^2. Since the deck is around the pool, it will have the same length and width as the pool plus the width of the deck on each side. The formula to calculate the area of the deck is:
Area of the deck = (length of the pool + 2 * width of the deck) * (width of the pool + 2 * width of the deck)
In this case, the length of the pool is 20m, the width of the pool is 10m, and the construction cost is $30/m^2. Based on the budget of $1920, we can calculate:
1920 = (20 + 2 * x) * (10 + 2 * x)
where x represents the width of the deck. By solving this equation, we can find the value of x.
B. Now, Helga's budget for the deck has increased to $6000. Following the same steps as above, we set up the equation:
6000 = (20 + 2 * x) * (10 + 2 * x)
Solving this equation will give us the updated width of the deck that fits within the new budget.
To find the solution for both questions, we need to simplify and solve the quadratic equation by multiplying it out and rearranging the terms. The final step will be to solve for x using factoring or using the quadratic formula.
Do you have any specific values for the width of the deck for either question?
deck length = 20
deck width = 10+2w
deck area = 20(10+2w) - 200 = 40 w
40 w (30) = 1920
w = 1.6 meters
1200 w = 6000
w = 5 meters