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

(10,10)
left parenthesis 10 comma 10 right parenthesis

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

(20,11.5)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \(25x + 15y \geq 200\), we will substitute each point into the inequality and check if it satisfies the condition.

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

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

3. For the point (20, 11.5): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] Since \(672.5 \geq 200\), it satisfies the inequality.

Thus, the points (10, 10) and (20, 11.5) are viable solutions. However, since you are asking for a single viable solution, the point (10, 10) has been identified early and satisfies the condition.

Conclusion: The point (10, 10) is a viable solution in this context.