Question

Use the image to answer the 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 (10,10) left parenthesis 10 comma 10 right parenthesis (20,11.5) left parenthesis 20 comma 11.5 right parenthesis 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 to the inequality \( 25x + 15y \geq 200 \), we will substitute each point into the inequality.

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

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

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

Based on the checks, both \( (10, 10) \) and \( (20, 11.5) \) are viable solutions to the inequality. Therefore, if the question only asks for one viable solution from the provided choices, you can choose either \( (10, 10) \) or \( (20, 11.5) \).

If you need to pick only one based on the phrasing of the question, you can conclude with: (10, 10) as a viable solution.