Question
This graph shows the inequality 25x+15y≥200, which represents the number of chairs and tables a carpenter can build, where x represents the number of chairs and y represents the number of tables. Which labeled points on the graph indicate a viable combination of chairs and tables that meets the carpenter's production goal?
(1 point)
Responses
(5, 2)
(5, 2)
None of the points are a viable solution
None of the points are a viable solution
(15, 4.5)
(15, 4.5)
(18, 10)
(18, 10)
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(1 point)
Responses
(5, 2)
(5, 2)
None of the points are a viable solution
None of the points are a viable solution
(15, 4.5)
(15, 4.5)
(18, 10)
(18, 10)
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Answers
GPT-4o mini
To determine which points satisfy the inequality \( 25x + 15y \geq 200 \), we will substitute each of the labeled points into the inequality:
1. **For the point (5, 2)**:
\[
25(5) + 15(2) = 125 + 30 = 155
\]
\[
155 \geq 200 \quad \text{(False)}
\]
2. **For the point (15, 4.5)**:
\[
25(15) + 15(4.5) = 375 + 67.5 = 442.5
\]
\[
442.5 \geq 200 \quad \text{(True)}
\]
3. **For the point (18, 10)**:
\[
25(18) + 15(10) = 450 + 150 = 600
\]
\[
600 \geq 200 \quad \text{(True)}
\]
Thus, the points (15, 4.5) and (18, 10) are viable combinations that meet the carpenter's production goal, while (5, 2) does not satisfy the inequality.
Therefore, the viable combinations are:
- (15, 4.5)
- (18, 10)
1. **For the point (5, 2)**:
\[
25(5) + 15(2) = 125 + 30 = 155
\]
\[
155 \geq 200 \quad \text{(False)}
\]
2. **For the point (15, 4.5)**:
\[
25(15) + 15(4.5) = 375 + 67.5 = 442.5
\]
\[
442.5 \geq 200 \quad \text{(True)}
\]
3. **For the point (18, 10)**:
\[
25(18) + 15(10) = 450 + 150 = 600
\]
\[
600 \geq 200 \quad \text{(True)}
\]
Thus, the points (15, 4.5) and (18, 10) are viable combinations that meet the carpenter's production goal, while (5, 2) does not satisfy the inequality.
Therefore, the viable combinations are:
- (15, 4.5)
- (18, 10)