b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 25 tons of rock to cover the area. If each ton cost $70 and each tree is $90, what is the maximum number of trees you can buy with a budget for rock and trees of $3,000? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
(25 * $70) + $90x < $3000
Can you explain how I got that inequality?
I hope this helps.
To solve this problem, we need to determine the maximum number of trees that can be bought within a given budget of $3,000, while also purchasing 25 tons of decorative rock.
Let's assume the maximum number of trees that can be bought is represented by the variable 'x'.
The cost of 25 tons of rock is 25 * $70 = $1750.
The cost of 'x' trees is 'x' * $90 = $90x.
So, the total cost of rock and trees is $1750 (for the rock) + $90x (for the trees).
To find the maximum number of trees 'x' that can be bought within the budget,
we set up the inequality:
$1750 + $90x ≤ $3000
Simplifying the inequality, we get:
$90x ≤ $3000 - $1750
$90x ≤ $1250
Dividing both sides of the inequality by $90, we get:
x ≤ $1250 / $90
x ≤ 13.88
Since the number of trees should be a whole number, we take the integer part of the result.
Therefore, the maximum number of trees that can be bought is 13.
The inequality x ≤ 13 tells us that the number of trees should be 13 or less to fit within the given budget.