Question

Brown's Tree Farm Company is going to plant pine trees and birch trees this planting season. On Farm A, the land type allows for them to plant 25 pine trees per acre and 75 birch trees per acre. On Farm B, the land type allows for them to plant 50 pine trees per acre and 75 birch trees per acre. There are a total of 200 pine trees and 450 birch trees available for planting.

1. Write and solve a system of equations to determine how many of each tree the company will plant on each farm.

Answer 1

Let x be the number of acres of Farm A planted with pine trees and birch trees, and let y be the number of acres of Farm B planted with pine trees and birch trees.

The system of equations would be as follows:

25x + 50y = 200 (the total number of pine trees planted)

75x + 75y = 450 (the total number of birch trees planted)

To solve this system of equations, we can use the method of substitution. Solving the first equation for x in terms of y:

x = (200 - 50y) / 25

We can substitute this expression for x into the second equation:

75((200 - 50y) / 25) + 75y = 450

Simplifying and solving for y:

(200 - 50y) + 75y = 450

25y = 250

y = 10

So 10 acres of Farm B are planted with pine and birch trees. To find the number of acres of Farm A that are planted with pine and birch trees, we can substitute this value of y back into the first equation:

25x + 50(10) = 200

25x = 50

x = 2

So 2 acres of Farm A are planted with pine and birch trees.

Therefore, the company will plant 25x = 50 pine trees and 75x = 225 birch trees on Farm A, and 50y = 500 pine trees and 75y = 750 birch trees on Farm B.