1) you are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.
Q1: write an inequality that demonstrates how much money you will be willing to spend on the project.
A1: 6,000 greater than > and equal = to 10,000
Q2: 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.
A2: 30(60) + 84x = 2500
1800 + 84x = 2500
subtract both sides by 1800 to get:
-1800 + 84x = 2500-1800
84x = 700
divide both sides by 84 to get:
x = 8.33
The first answer I don't understand at all.
I would do this...
6000<amountIspend<=10000
In this particular class the answer I believe to be true is in an equation form, not with words.
My answer would be
$6,000 <(underline this)$10,000
and that's it.
P <= $10,000 + => $6,000
To answer Q2 and find the maximum number of trees you can buy with a budget of $2,500, you need to set up an equation and solve for the number of trees, which we'll represent as 'x'.
First, let's break down the cost components. You are buying 30 tons of rock, and each ton costs $60. The total cost of the rock will be 30 tons multiplied by $60 per ton, which gives us 30 * $60 = $1800.
Next, you'll need to consider the cost of the trees. Each tree costs $84. Since you want to find the maximum number of trees you can buy with a budget of $2,500, we'll subtract the cost of the rock from the total budget to find the remaining amount for the trees.
So, subtracting the cost of the rock ($1800) from the total budget ($2500), we get $2500 - $1800 = $700.
Now, we can set up the equation: 84x = 700, where 'x' represents the number of trees we are trying to find.
To solve for 'x', divide both sides of the equation by 84:
84x / 84 = 700 / 84
Simplifying, we have:
x = 8.33
Since 'x' represents the number of trees, we cannot have a fraction of a tree. So, the maximum number of trees you can buy with a budget of $2,500 is 8.