Question

9.

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

choose only one answer

Answer 2

To determine which labeled points (if any) satisfy the inequality \(25x + 15y \geq 200\), we can evaluate each point by substituting the x and y values into the inequality.

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

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

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

Based on this analysis, the points which indicate a viable combination of chairs and tables that meets the carpenter's production goal are:

- (15, 4.5)
- (18, 10)

So the correct response would be: **(15, 4.5)** and **(18, 10)**.