You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.
Write an inequality that demonstrates how much money you will be willing to spend on the project.
Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer
$6,000≤x≤$10,000 where x is total amount
Well your 30 tons of rock will cost
30 * $60 = $1800
so you are left with
2500 - 1800 = 700 for trees
700/84 = 8 1/3 but 1/3 of a tree will not do so we can only buy 8 trees
y ≤ 8 where y is the number of trees
b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
The coordinate graph of the backyard shows the location of trees, plants, the patio, and utility lines. (If necessary, you may copy and paste the image to another document and enlarge it.)
To find the maximum number of trees you can buy with a budget of $2,500, we need to determine the amount spent on rocks and subtract it from the budget, and then divide the remaining amount by the cost of each tree.
Let's first calculate the total cost of the rocks. Since each ton costs $60 and we need 30 tons, the total cost of the rocks is:
30 tons * $60/ton = $1800
Now, let's calculate the amount of money remaining from the budget for trees:
Remaining amount = Budget - Cost of Rocks = $2500 - $1800 = $700
We can then determine the maximum number of trees we can buy by dividing the remaining amount by the cost of each tree:
Maximum number of trees = Remaining amount / Cost of each tree = $700 / $84/tree = 8.333
Since you cannot buy a fraction of a tree, the maximum whole number of trees you can buy is 8.
To write an inequality that illustrates the problem, we can use the variable "t" to represent the number of trees you want to buy, and the inequality would be:
t ≤ 8
This inequality represents that the number of trees you can buy must be less than or equal to 8.