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?

Question

(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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Answer 1

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)