For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget 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.
Would 5 be a solution to the inequality? Justify your answer.
Five is not the answer.
You need to spend 30x60 = $1800 on rocks. That leaves you with $700 for trees.
The maximum number of trees you can buy is the largest integer x that satsifies
84 x <or= 1500
x = 17
What is wrong with my math?
700 / 84 = 8.33
Ms Sue is right. I don't know where the 1500 number came from. My mind was wandering
To find the maximum number of trees you can buy with a budget of $2,500, we need to set up an inequality.
Let's assume we can buy x number of trees. Each tree costs $84, so the total cost of buying x trees would be 84x dollars.
The budget we have is $2,500. To find an inequality, we need to compare the total cost of the trees to the budget. We want the cost of the trees to be less than or equal to the budget.
So the inequality would be:
84x ≤ 2500
Now, let's solve the inequality:
Divide both sides of the inequality by 84:
x ≤ 2500/84
Now, we can calculate the value of x:
x ≤ 29.76...
Since x represents the number of trees, it cannot be a decimal or fraction. Therefore, the maximum number of trees you can buy is 29.
To justify this answer, we can substitute 5 into the inequality:
84(5) = 420
Is 420 less than or equal to 2500? Yes, it is. So 5 is indeed a valid solution to the inequality. Therefore, you can buy at least 5 trees with a budget of $2,500.