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 (2,3) left parenthesis 2 comma 3 right parenthesis None of the points are a viable solution.

Answer 1

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

1. For the point (10, 10): \[ 25(10) + 15(10) = 250 + 150 = 400 \] Since \( 400 \geq 200 \) is true, (10, 10) 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, (20, 11.5) is also a viable solution.

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

Given this analysis, both (10, 10) and (20, 11.5) are viable solutions. If you have to select only one, you can pick either of them. If you specifically want one point as the answer, you can choose (10, 10) as it is included first. However, since the question might imply that exactly one point is asked for, the response might vary based on the context provided.

But most accurately, if only one response is to be chosen based on the clarity you provided, the point (10, 10) is a viable solution.