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.

Question

Determine which of these points are viable combinations that meet the designer's production goal,

(1 point)
Responses

(2,10)
(2,10)

None of the points are a viable solution
None of the points are a viable solution

(3,8)
(3,8)

(4,6)
(4,6)

(6,2)
(6,2)
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Answer 1

To determine whether the points (2,10), (3,8), (4,6), and (6,2) meet the production goal defined by the inequality \( 25x + 15y \geq 200 \), we will substitute each point into the inequality.

1. For the point (2,10): \[ 25(2) + 15(10) = 50 + 150 = 200 \] Since \( 200 \geq 200 \) is true, (2,10) meets the goal.

2. For the point (3,8): \[ 25(3) + 15(8) = 75 + 120 = 195 \] Since \( 195 \geq 200 \) is false, (3,8) does not meet the goal.

3. For the point (4,6): \[ 25(4) + 15(6) = 100 + 90 = 190 \] Since \( 190 \geq 200 \) is false, (4,6) does not meet the goal.

4. For the point (6,2): \[ 25(6) + 15(2) = 150 + 30 = 180 \] Since \( 180 \geq 200 \) is false, (6,2) does not meet the goal.

Based on this evaluation, the only viable combination that meets the designer's production goal is the point (2,10). Therefore, the other points are not viable solutions.

In conclusion, the correct response is that (2,10) is the only viable solution that meets the designer's production goal.