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 (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. (20,11.5) left parenthesis 20 comma 11.5 right parenthesis (10,10)

Answer 1

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

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

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

Out of the given options, both \( (20, 11.5) \) and \( (10, 10) \) are viable solutions. However, if you are asked to select only one, the point \( (20, 11.5) \) is certainly valid based on the calculations.

Thus, the answer is: (20, 11.5)