Nick budgets from 300 pesos to 900 pesos for trees and/or bushes to landscape his yard. After shopping around, he finds that good trees cost 150 pesos and mature bushes cost 75 pesos. What combination of trees and/or bushes can he afford to buy?
Note that each tree costs the same as 2 bushes.
Nick can buy 2-6 trees and 0 bushes, or
4-12 bushes and 0 trees.
Each tree can be replaced by two bushes, so it's fairly easy to see how to keep within budget by replacing each tree by 2 bushes.
To find out what combination of trees and/or bushes Nick can afford to buy, let's set up an equation based on his budget.
Let's assume Nick buys 'x' trees and 'y' bushes.
The cost of each tree is 150 pesos, and Nick wants to buy 'x' trees. So the total cost of trees would be 150 * x pesos.
Similarly, the cost of each mature bush is 75 pesos, and Nick wants to buy 'y' bushes. So the total cost of bushes would be 75 * y pesos.
According to the information given, Nick has a budget ranging from 300 to 900 pesos. Therefore, we can set up the following inequality:
300 pesos ≤ (150 * x) + (75 * y) ≤ 900 pesos
Now, let's simplify the inequality:
300 pesos ≤ 150x + 75y ≤ 900 pesos
To make it easier to work with, let's divide the entire inequality by 75:
4 pesos ≤ 2x + y ≤ 12 pesos
Now, let's examine the possible combinations of trees and bushes that Nick can afford.
1. If Nick buys the minimum number of trees (0) and the maximum number of bushes (12), the total cost would be (150 * 0) + (75 * 12) = 900 pesos.
2. If Nick buys the maximum number of trees (4) and the minimum number of bushes (0), the total cost would be (150 * 4) + (75 * 0) = 600 pesos.
3. If Nick buys 1 tree and 10 bushes, the total cost would be (150 * 1) + (75 * 10) = 900 pesos.
4. If Nick buys 2 trees and 8 bushes, the total cost would be (150 * 2) + (75 * 8) = 900 pesos.
5. If Nick buys 3 trees and 6 bushes, the total cost would be (150 * 3) + (75 * 6) = 900 pesos.
6. If Nick buys 4 trees and 4 bushes, the total cost would be (150 * 4) + (75 * 4) = 900 pesos.
7. If Nick buys 5 trees and 2 bushes, the total cost would be (150 * 5) + (75 * 2) = 900 pesos.
8. If Nick buys the minimum number of trees (0) and the minimum number of bushes (0), the total cost would be (150 * 0) + (75 * 0) = 0 pesos.
Therefore, Nick has several combinations of trees and bushes that he can afford to buy: (0 trees, 12 bushes), (4 trees, 0 bushes), (1 tree, 10 bushes), (2 trees, 8 bushes), (3 trees, 6 bushes), (4 trees, 4 bushes), (5 trees, 2 bushes), and (0 trees, 0 bushes).