For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 25 tons of rock to cover the area. If each ton costs $62 and each tree is $76, what is the maximum number of trees you can buy with a budget of $2,000? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
25*62 + 76 n </= 2000
1550 + 76 n </= 2000
76 n </= 450
solve as equality and get n = 5.92
well we can not plant .92 of a tree, so we can not plant more than 5
however we can plant less
so
n </= 5
wow, thanks Damon it's open book, I have all the right numbers and have been reading over my notes and I could not put it together, Thanks.
To solve this problem, we need to set up an inequality that represents the given conditions and then solve it to find the maximum number of trees that can be bought within the budget.
Let's assume that the number of trees that can be bought is represented by the variable "t".
The cost of each tree is $76, and we want to find the maximum number of trees that can be bought with a budget of $2,000.
Therefore, the inequality representing this situation is:
76t ≤ 2000
Next, we need to solve this inequality to find the value of "t" that satisfies the condition.
Dividing both sides of the inequality by 76, we have:
t ≤ 2000/76
Calculating the right side of the inequality, we have:
t ≤ 26.3158 (rounded to four decimal places)
Since the number of trees cannot be a decimal fraction, the maximum number of trees that can be purchased within the budget is 26.
Therefore, the maximum number of trees that can be bought with a budget of $2,000 is 26.