A garden designer is working on a project where they need to produce a certain number of flower beds and garden paths. The inequality 25x+15y≥200 represents the production goal, where x is the number of flower beds and y is the number of garden paths. The graph below shows various points on a coordinate plane, with each point representing a possible combination of flower beds and garden paths.Determine which of these points are viable combinations that meet the designer's production goal,

Question

(2,10)
None of the points are a viable solution
(3,8)
(4,6)
(6,2)

Answer 1

To determine which points meet the designer's production goal represented by the inequality \( 25x + 15y \geq 200 \), we will substitute each point into the inequality and check if it satisfies the condition.

1. Point (2, 10): \[ 25(2) + 15(10) = 50 + 150 = 200 \] Since \( 200 \geq 200 \) is true, (2, 10) is a viable solution.

2. Point (3, 8): \[ 25(3) + 15(8) = 75 + 120 = 195 \] Since \( 195 \geq 200 \) is false, (3, 8) is not a viable solution.

3. Point (4, 6): \[ 25(4) + 15(6) = 100 + 90 = 190 \] Since \( 190 \geq 200 \) is false, (4, 6) is not a viable solution.

4. Point (6, 2): \[ 25(6) + 15(2) = 150 + 30 = 180 \] Since \( 180 \geq 200 \) is false, (6, 2) is not a viable solution.

After checking all the points, the only viable combination that meets the designer's production goal is (2, 10).

Thus, the answer is:

• Viable points: (2, 10)
• Non-viable points: (3, 8), (4, 6), (6, 2)