Question

Use the image to answer the question. This graph shows the inequality 25x+15y≥20025x+15y≥200 , representing Adela's earnings for lawn mowing and dog walking, where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points on the graph is a viable solution in this context? (1 point) Responses (10, 10) (10, 10) (20, 11.5) (20, 11.5) (2, 3) (2, 3) None of the points labeled on the graph are a viable solution. None of the points labeled on the graph are a viable solution. Skip to navigation Item 1 , Fully Attempted. Item 2 , Fully Attempted. Item 3 , Fully Attempted. Item 4 , Fully Attempted. Item 5 , Unattempted. Previous Review

Answer 1

To determine which of the labeled points on the graph is a viable solution for the inequality \( 25x + 15y \geq 200 \), we need to evaluate each point against the inequality.

1. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
\( 400 \geq 200 \) (True)

2. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
\( 672.5 \geq 200 \) (True)

3. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
\( 95 \geq 200 \) (False)

Therefore, points (10, 10) and (20, 11.5) satisfy the inequality, while (2, 3) does not.

Based on your question, both (10, 10) and (20, 11.5) are viable solutions. However, if you can select only one, the first point (10, 10) is valid as it is still within the bounds of the inequality.

So, if you need to select only one point, the conclusion is:

- **Viable Solutions**: (10, 10) and (20, 11.5)
- Your answer should be either (10, 10) or (20, 11.5), depending on the specific requirements or the question asked about the graph.