Question
This graph shows the inequality 25x+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?
(2,3)(10,10)(20,11.5)
the shaded part of the graph is on the right of the full line.
(1 point)
Responses
(10, 10)
(10, 10)
(20, 11.5)
(20, 11.5)
None of the points labeled on the graph are a viable solution.
None of the points labeled on the graph are a viable solution.
(2, 3)
, 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?
(2,3)(10,10)(20,11.5)
the shaded part of the graph is on the right of the full line.
(1 point)
Responses
(10, 10)
(10, 10)
(20, 11.5)
(20, 11.5)
None of the points labeled on the graph are a viable solution.
None of the points labeled on the graph are a viable solution.
(2, 3)
Answers
GPT-4o mini
To determine which point is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can substitute the coordinates of each point into the inequality and check whether it holds true.
### Testing the points:
1. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \( 95 < 200 \), this point does not satisfy the inequality.
2. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \( 400 \geq 200 \), this point satisfies the inequality.
3. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \( 672.5 \geq 200 \), this point also satisfies the inequality.
### Conclusion:
Both (10, 10) and (20, 11.5) are viable solutions, but since the question asks for which of the labeled points is a viable solution, you can select either of these two.
Therefore, the best response would be:
- **(10, 10)** or **(20, 11.5)** (as both points are valid solutions). If you have to choose one, either is correct based on your labeling.
### Testing the points:
1. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \( 95 < 200 \), this point does not satisfy the inequality.
2. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \( 400 \geq 200 \), this point satisfies the inequality.
3. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \( 672.5 \geq 200 \), this point also satisfies the inequality.
### Conclusion:
Both (10, 10) and (20, 11.5) are viable solutions, but since the question asks for which of the labeled points is a viable solution, you can select either of these two.
Therefore, the best response would be:
- **(10, 10)** or **(20, 11.5)** (as both points are valid solutions). If you have to choose one, either is correct based on your labeling.