Question

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,

(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)

Answer 1

To determine which points are viable combinations that meet the designer's production goal represented by the inequality \(25x + 15y \geq 200\), we can test each point one by one by substituting the values of \(x\) and \(y\) into the inequality.

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.

**Summary**: The only viable combination that meets the designer's production goal is \((2, 10)\).