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.

Question

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.

Answer 1

Cost of landscaping = 30(60) + 84T

1800 + 84T = 2500

84T = 700

T = 8.333

8 Trees maximum

Answer 2

To solve this problem, we first need to set up an inequality that represents the budget for both the rock and trees.

Let's assume the number of trees as 'x'.

The cost of rock needed is given as 30 tons, and each ton costs $60. So, the cost of the rock is 30 * 60 = $1800.

The cost of 'x' trees can be calculated as 'x' multiplied by the cost of each tree, which is $84.

Therefore, the inequality representing the total budget is:
$1800 + $84x ≤ $2500

Now, we solve this inequality to find the maximum number of trees 'x' that can be bought within the given budget of $2500.

$1800 + $84x ≤ $2500

To isolate 'x', we need to subtract $1800 from both sides:

$84x ≤ $700

Finally, divide both sides by $84:

x ≤ $700 / $84

Simplifying:

x ≤ 8.33

Since the number of trees cannot be fractional, the maximum number of trees that can be bought within the given budget is 8 trees.