Question

Anton wants to plant a small orchard of apple trees and cherry trees in his backyard. He has a budget of $1,000, and his plot has a maximum of 100 square feet. The apple trees he wants cost $40 each and require 5 square feet. The cherry trees he wants cost $50 each and require 4 square feet. Which system of inequalities correctly represents this situation where a is the number of apple trees and c is the number of cherry trees that Anton can plant in his orchard?

Answer 1

The system of inequalities that correctly represents the situation is: 40a + 50c ≤ 1000 and 5a + 4c ≤ 100.

Step-by-step explanation:

The number of apple trees Anton can plant will be represented by the variable 'a' and the number of cherry trees by the variable 'c'. The cost of each apple tree is $40 and the cost of each cherry tree is $50. So the total cost of apple trees will be 40a and the total cost of cherry trees will be 50c.

The maximum square footage required for apple trees is 5 square feet, so the total square footage for apple trees will be 5a. The maximum square footage required for cherry trees is 4 square feet, so the total square footage for cherry trees will be 4c.

Since Anton has a maximum budget of $1,000, the total cost of apple trees plus the total cost of cherry trees must be less than or equal to $1,000. So we have the inequality: 40a + 50c ≤ 1000.

Since the maximum square footage available is 100 square feet, the total square footage for apple trees plus the total square footage for cherry trees must be less than or equal to 100. So we have the inequality: 5a + 4c ≤ 100.