Question

This graph shows the inequality 25x+15y≥200 , and represents Lina’s earnings for lawn mowing and dog walking where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?

(1 point)
Responses

(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis

(2,3)
left parenthesis 2 comma 3 right parenthesis

None of the points are a viable solution.
None of the points are a viable solution.

(10,10)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we will evaluate each point individually.

1. For the point \( (20, 11.5) \):
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \( 672.5 \geq 200 \), this point satisfies the inequality.

2. For the point \( (2, 3) \):
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \( 95 < 200 \), this point does not satisfy the inequality.

3. For the point \( (10, 10) \):
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \( 400 \geq 200 \), this point satisfies the inequality as well.

Based on the evaluations:
- \( (20, 11.5) \) is a viable solution.
- \( (2, 3) \) is not a viable solution.
- \( (10, 10) \) is a viable solution.

Thus, two points, \( (20, 11.5) \) and \( (10, 10) \), are viable solutions. Since the question asks for "which of the labeled points is a viable solution," if we assume that the options are only those listed, then both \( (20, 11.5) \) and \( (10, 10) \) would be correct viable solutions.

Given the choices:
- If the instructions are to select only one point, the first option \( (20, 11.5) \) is a viable solution.