1. 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 $40 and each tree is $65, what is the minimum number of trees you can buy with a budget for rock and trees of at least $2,750? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

Question

1. 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 $40 and each tree is $65, what is the minimum number of trees you can buy with a budget for rock and trees of at least $2,750? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

I am not very good at trying to write inequalities. I always think I have it right then I always find out I am wrong. Any help would be appreciated.

Answer 1

let the number of tons of rock be x

let the number of trees be y

40x + 65y ≤ 2750

also x ≤ 25

Explanation: I just translated the "English" into "Math"

Answer 2

Thank you so very much this is a big help

Answer 3

Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 40 tons of rock to cover the area. If each ton cost $70 and each tree is $94, what is the minimum number of trees you can buy with a budget for rock and trees of at least $4,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

Answer 4

To solve this problem, let's break it down step by step:

First, let's define our variables:
Let's say the number of trees you buy is 't'.

Now, let's see how we can write the inequality:

To find the minimum number of trees you can buy, we need to make sure we have enough money for both the rocks and the trees. We know that each ton of rock costs $40, and we need 25 tons, so the cost of the rocks is 40 * 25 = $1000.

We also know that each tree costs $65, and we want to buy 't' trees. So the cost of the trees is 65 * t.

The total budget for rocks and trees is $2,750. Therefore, our inequality can be written as:

Cost of rocks + Cost of trees ≤ Total budget
1000 + 65 * t ≤ 2750

Now that we have our inequality, let's solve it:

1000 + 65 * t ≤ 2750

First, subtract 1000 from both sides to isolate the term with 't':

65 * t ≤ 2750 - 1000
65 * t ≤ 1750

Next, divide both sides by 65 to solve for 't':

t ≤ 1750 / 65
t ≤ 26.92

Since we can't buy a fraction of a tree, we need to round down to the nearest whole number. Therefore, the minimum number of trees you can buy is 26.

So, the inequality is t ≤ 26, meaning you can buy at most 26 trees with a budget of at least $2,750 for rocks and trees.