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.
The line goes from (0,10) to (8,0)
(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.
The line goes from (0,10) to (8,0)
(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 points are viable solutions to the inequality \(25x + 15y \geq 200\), we can test each point in the inequality.
1. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \(95 < 200\), this point is **not** a viable solution.
2. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \(400 \geq 200\), this point **is** a viable solution.
3. **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.
Given that (10, 10) is a viable solution, and (20, 11.5) is also viable, but less direct in the context of the problem, the best choice among the options provided is:
**(10, 10)**
1. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \(95 < 200\), this point is **not** a viable solution.
2. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \(400 \geq 200\), this point **is** a viable solution.
3. **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.
Given that (10, 10) is a viable solution, and (20, 11.5) is also viable, but less direct in the context of the problem, the best choice among the options provided is:
**(10, 10)**