To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we will plug each point into the inequality.
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Point A: (10, 10) \[ 25(10) + 15(10) = 250 + 150 = 400 \] Since \( 400 \geq 200 \), this point satisfies the inequality.
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Point B: (2, 3) \[ 25(2) + 15(3) = 50 + 45 = 95 \] Since \( 95 < 200 \), this point does not satisfy the inequality.
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Point D: (20, 11.5) \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] Since \( 672.5 \geq 200 \), this point satisfies the inequality.
Now we summarize:
- Point A: (10, 10) is a viable solution.
- Point B: (2, 3) is not a viable solution.
- Point D: (20, 11.5) is a viable solution.
Since both points A and D are viable, but the options do not provide a choice for both, we can conclude that at least one point (A or D) is viable.
From the options provided, the answer would be:
A. (10, 10) is a viable solution, and is one of the correct answers.
However, since D (20, 11.5) is also a viable solution but was not listed in the choices, the best answer with the options is C. None of the points are a viable solution, cannot be chosen as there are viable points; hence the conclusion shows that A is the first valid answer.
The correct interpretation is therefore that A. (10, 10) is indeed a viable solution in the context!