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?

Question

(1 point)
Responses

(2,3)
left parenthesis 2 comma 3 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.

(10,10)

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.

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

2. 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.

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

Based on these evaluations, the viable solutions in this context are the points (20, 11.5) and (10, 10). However, since there can only be one response, the correct answer according to the options given should be:

(20, 11.5).