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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Answer 1

To determine which points satisfy the inequality \( 25x + 15y \geq 200 \), we can substitute the coordinates of each point into this inequality and check if it holds true.

1. For the point **(5, 2)**:
\[
25(5) + 15(2) = 125 + 30 = 155
\]
\( 155 \geq 200 \) is **false**.

2. For the point **(15, 4.5)**:
\[
25(15) + 15(4.5) = 375 + 67.5 = 442.5
\]
\( 442.5 \geq 200 \) is **true**.

3. For the point **(18, 10)**:
\[
25(18) + 15(10) = 450 + 150 = 600
\]
\( 600 \geq 200 \) is **true**.

So, the viable combinations of chairs and tables that meet the carpenter's production goal are:

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

The correct response would indicate that the points (15, 4.5) and (18, 10) are viable solutions, and (5, 2) is not.