Question

Maple Grove wants to include two types of pale trees, the namesake of the city, for their parks. Two varieties of maple trees have been selected. One variety costs $80 per tree, the other more colorful variety costs $85 per tree. The tree budget must not exceed $76,000. Citizens want more of the colorful $85 trees than the others if possible. How many trees of each variety can Maple Grove afford to purchase?

Answer 1

To determine the number of trees of each variety Maple Grove can afford to purchase, a system of equations needs to be set up. By solving this system, it can be determined that Maple Grove can afford to purchase approximately 5,263 trees of the $80 variety and 21,737 trees of the $85 variety.

Step-by-step explanation:

To determine how many trees of each variety Maple Grove can afford to purchase, we need to set up a system of equations. Let's denote the number of $80 trees as x, and the number of $85 trees as y. The total cost of the trees should not exceed $76,000. We can set up the following equations:

x + y ≤ 76,000 (equation 1)

85y ≤ 80x (equation 2)

We can solve this system of equations to find the values of x and y. Since the citizens want more of the $85 trees, we can assume x is greater than y. By substituting y = 76,000 - x into equation 2 and solving, we find that x ≈ 5,263 and y ≈ 21,737. Therefore, Maple Grove can afford to purchase approximately 5,263 trees of the $80 variety and 21,737 trees of the $85 variety.