1. You are planning to spend no more than $10,000 and no less than $8,000 on your landscaping project.
a. Write an inequality that demonstrates how much money you will are willing to spend on the project.
b. For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $80 and each tree is $104, what is the maximum number of trees you can buy with a budget of $3,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
c. Would twelve trees be a solution to the inequality in Part b? Justify your answer.
a. $8,000 < x < $10,000
b. $3,500 - 30($80) > $104x
I'll leave the rest to you.
a. $8,000 <= X =< $10,000.
b. $104X + $80*30 <= $3500,
104X + 2400 <=3500,
104X <= 3500 - 2400,
104X <= 1100,
X<=10.6,
Or
X = 10 = Max. he can buy.
a. The inequality that demonstrates how much money you are willing to spend on the landscaping project is:
$8,000 ≤ money spent ≤ $10,000
b. Let's solve the problem step by step. We know that each ton of rock costs $80, and we need 30 tons of rock. So the total cost of the rocks is:
Cost of rocks = 30 tons * $80 = $2400
We also know that each tree costs $104, and we want to find the maximum number of trees we can buy with a budget of $3,500. Let's say the number of trees we can buy is t. We can express the total cost of the trees as:
Cost of trees = t * $104
According to the problem, the total cost of the project should not exceed $3,500. So we can write the inequality as:
Cost of rocks + Cost of trees ≤ $3,500
Substituting the values we found earlier:
$2400 + t * $104 ≤ $3,500
Simplifying the inequality:
$2400 + 104t ≤ $3,500
Now, let's solve for t:
104t ≤ $3,500 - $2400
104t ≤ $1,100
t ≤ $1,100 / 104
t ≤ 10.58
Since the number of trees must be a whole number, the maximum number of trees you can buy is 10.
c. No, twelve trees would not be a solution to the inequality in Part b. The maximum number of trees that can be bought with a budget of $3,500 is 10. Twelve trees would exceed the budget and violate the inequality.