This graph shows the inequality 25x+15y≥200

Question

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

(10, 10)
(10, 10)

(20, 11.5)
(20, 11.5)

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

(2, 3)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can substitute each point into the inequality to see if it holds true.

1. For the point \( (10, 10) \): \[ 25(10) + 15(10) = 250 + 150 = 400 \] Since \( 400 \geq 200 \) is true, this point is a viable solution.

2. For the point \( (20, 11.5) \): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] Since \( 672.5 \geq 200 \) is true, this point is also a viable solution.

3. For the point \( (2, 3) \): \[ 25(2) + 15(3) = 50 + 45 = 95 \] Since \( 95 \geq 200 \) is not true, this point is not a viable solution.

Based on this analysis, both points \( (10, 10) \) and \( (20, 11.5) \) are viable solutions, while the point \( (2, 3) \) is not.

Given the provided options, if the response must only be one viable solution, the correct answer could be either of the first two options, but without any specific conditions, we conclude that both \( (10, 10) \) and \( (20, 11.5) \) are viable solutions.

If the question requires just one of the available options, please choose either \( (10, 10) \) or \( (20, 11.5) \). Otherwise, you could also mention that multiple points are viable.