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Bot GPT 4-o mini To determine which of the labeled points is a viable solution to the inequality \(25x + 15y \geq 200\), we need to evaluate each point by substituting the coordinates into the inequality.
1. For the point (20, 11.5):
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \(672.5 \geq 200\), this point is a viable solution.
2. For the point (10, 10):
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \(400 \geq 200\), 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 the evaluation, both (20, 11.5) and (10, 10) are viable solutions. Since the question asks for one viable solution and both are valid:
The best answer from the given options would be:
- (20, 11.5) or (10, 10) depending on whether you need to select one or both. If you must choose one, either is valid based on the context given.
However, if only one option needs to be provided from the response choices, you can select either (20, 11.5) or (10, 10) as they both satisfy the inequality. If the choice of "None of the points are a viable solution" is also included, this option would be incorrect since viable solutions exist.