I am confuse as to how to actually work these problems. Please help!!!
1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.
a) Write an inequality that demonstrates how much money you will be willing to spend on the project.
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
what are the problems?
a) To write an inequality that demonstrates how much money you are willing to spend on the project, we can use the variable "x" to represent the amount of money you are willing to spend. The inequality can be written as:
$6,000 ≤ x ≤ $10,000
This means that the amount you are willing to spend (x) must be between $6,000 and $10,000, inclusive.
b) To determine the maximum number of trees you can buy with a budget of $2,500 for rock and trees, we need to set up an inequality based on the given information.
Let's assume you buy "t" trees. The cost of the rock is given by 30 tons multiplied by the cost per ton, which is $60. So the cost of the rock is 30 * $60 = $1800.
The cost of "t" trees is given by "t" multiplied by the cost per tree, which is $84. Therefore, the cost of the trees is t * $84 = $84t.
To find the maximum number of trees you can buy, we need to find the maximum value of "t" such that the total cost (the cost of the rock plus the cost of the trees) is within the budget of $2,500.
The inequality can be written as:
1800 + 84t ≤ 2500
To solve this inequality for "t," we need to isolate "t" on one side of the inequality.
First, we subtract 1800 from both sides to get:
84t ≤ 700
Then, we divide both sides of the inequality by 84 to get:
t ≤ 8.33
Since we can't buy a fraction of a tree, we must round down to the nearest whole number. Therefore, the maximum number of trees you can buy is 8.
The inequality can be written as:
t ≤ 8