Question

There are two types of trees: elm and pine. There should be at least 16 total trees but no more than 30. The ratio of elm trees to pine trees will be 3:2. Give an example of how many trees of each type the designer could plan for the park. Show or explain how you found your answer.

Answer 1

Answer:Therefore, an example of how many trees the designer could plan for the park is 10 elm trees and 6 pine trees, totaling 16 trees.

Explanation:

Let's assume the total number of trees is 16. To find the number of elm trees, we can divide 16 by the sum of the ratio's parts (3 + 2 = 5) and then multiply the result by the first part of the ratio (3/5 * 16 = 9.6). Since we can't have a fraction of a tree, we round it to the nearest whole number, which gives us 10 elm trees.

Similarly, we can find the number of pine trees by multiplying the number of elm trees by the second part of the ratio (2/5 * 16 = 6.4). Again, rounding it to the nearest whole number, we have 6 pine trees.

Answer 2

Answer: 18 pine trees / 12 elm trees

Explanation:

To meet the requirement of at least 16 but no more than 30 trees with a 3:2 ratio of elm to pine trees, we can choose:

Elm Trees: 3x

Pine Trees: 2x

Where x is a positive integer. To stay within the given constraints:

3x + 2x ≥ 16 (at least 16 trees)

5x ≥ 16

x ≥ 16/5

x ≥ 3.2

We need to find the largest integer value for x while staying below 30 (no more than 30 trees). Since x must be an integer, the largest valid value for x is 6 (as 7 would exceed 30).

So, for the example:

Elm Trees = 3x = 3 * 6 = 18

Pine Trees = 2x = 2 * 6 = 12

In this case, there would be 18 elm trees and 12 pine trees, totaling 30 trees, which falls within the range of at least 16 but no more than 30 trees and maintains the 3:2 ratio of elm to pine trees.