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

30 tons of rock x 60 dollars = _____ dollars?

Subract that from 2500 to see how much is left over, then divide by 84 to see how many trees can be purchased.

You will need to decide how to write an inequality, but this seems like a very straightforward problem.

=)

Let's first calculate the cost of the rock. 30 tons of rock at $60 per ton would cost:

30 tons x $60/ton = $1800.

After purchasing the rock, we will have $2500 - $1800 = $700 left for trees.

Now, let's determine the maximum number of trees we can buy with $700. Each tree costs $84, so the inequality representing this situation would be:

$84x ≤ $700,

where "x" represents the number of trees.

To solve this inequality, we divide both sides by $84:

x ≤ $700 / $84,

x ≤ 8.333...

Since we cannot purchase a fraction of a tree, we need to round down to the nearest whole number. Therefore, the maximum number of trees we can buy is 8.

In conclusion, the maximum number of trees that can be bought with a budget of $2,500 for rock and trees is 8.

Let's denote the maximum number of trees that can be bought as 't'.

The cost of rock required to cover the area is calculated by multiplying the number of tons needed (30) by the cost per ton ($60). Therefore, the cost of the decorative rock is 30 x $60 = $1800.

Since the total budget for rock and trees is $2500, the remaining budget for buying trees can be calculated by subtracting the cost of rock from the total budget: $2500 - $1800 = $700.

Now, to determine the maximum number of trees that can be bought, we divide the remaining budget ($700) by the cost of each tree ($84): $700 ÷ $84 = 8.33.

Since we cannot purchase a fraction of a tree, we need to round down to the nearest whole number. Therefore, the maximum number of trees that can be bought is 8.

To summarize:

Inequality: 84t ≤ 700

Explanation: We set up an inequality that states the cost of the trees (84) multiplied by the maximum number of trees (t) should not exceed the remaining budget after purchasing the rock ($700). This ensures that the total cost of the trees does not exceed the available budget. By dividing both sides of the inequality by 84, we can determine the maximum number of trees that satisfies the given budget constraint.

To solve this problem, we can set up an inequality to represent the budget for rock and trees.

Let's assume the number of trees you can buy is represented by the variable "t".

The cost of the rocks can be calculated as follows: 30 tons of rock * $60/ton = $1800.

Now, let's set up the inequality:

$1800 + $84t ≤ $2500

We add the cost of the rocks and the cost of the trees to represent the total cost, and set it to be less than or equal to the budget of $2500.

To solve the inequality, we can isolate the variable "t" by subtracting $1800 from both sides of the inequality:

$84t ≤ $2500 - $1800

Simplifying further:

$84t ≤ $700

To get the value of "t", we divide both sides of the inequality by $84:

t ≤ $700 / $84

t ≤ 8.333...

Since you can't buy a fraction of a tree, we round down to the nearest whole number.

Therefore, the maximum number of trees you can buy with a budget of $2500 is 8 trees.