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Question

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)

Answer 1

To determine which labeled points on the graph indicate a viable combination of chairs (x) and tables (y) that meets the inequality \( 25x + 15y \geq 200 \), we can substitute the coordinates of each point into the inequality and check if it holds true.

1. Point (5, 2): \[ 25(5) + 15(2) = 125 + 30 = 155 \] \( 155 < 200 \) (not a viable solution)

2. Point (15, 4.5): \[ 25(15) + 15(4.5) = 375 + 67.5 = 442.5 \] \( 442.5 \geq 200 \) (viable solution)

3. Point (18, 10): \[ 25(18) + 15(10) = 450 + 150 = 600 \] \( 600 \geq 200 \) (viable solution)

Based on the calculations:

• (5, 2) is not a viable solution.
• (15, 4.5) is a viable solution.
• (18, 10) is a viable solution.

Thus, the viable combinations of chairs and tables are at points (15, 4.5) and (18, 10).

Answer 2

choose one

Answer 3

The point that indicates a viable combination of chairs and tables that meets the carpenter's production goal is:

(15, 4.5).