Question

This graph shows the inequality 25x+15y≥200 , and represents Lina’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 is a viable solution in this context? (1 point) Responses None of the points are a viable solution. None of the points are a viable solution. (10,10) left parenthesis 10 comma 10 right parenthesis (20,11.5) left parenthesis 20 comma 11.5 right parenthesis (2,3)

Answer 1

To determine which points are viable solutions for the inequality \( 25x + 15y \geq 200 \), we can substitute each point into the inequality and see if it satisfies it.

1. **For the point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \( 400 \geq 200 \), this point is a viable solution.

2. **For the point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \( 672.5 \geq 200 \), this point is also a viable solution.

3. **For the point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \( 95 < 200 \), this point is not a viable solution.

Based on this analysis, both **(10, 10)** and **(20, 11.5)** are viable solutions. However, since the question asks for which **labeled point is a viable solution** and does not ask for all viable solutions, either option could be considered correct depending on the context provided.

If you can choose only one point and based on common scenarios in such questions, it seems that (20, 11.5) likely represents a more productive outcome. But you could also just confirm the context with your instructor or the specific labeling used in the problem.

***Conclusion:***
Both (10, 10) and (20, 11.5) are viable solutions. (2,3) is not. If needed to select one, you can choose either depending on the focus of your answer.