This graph shows the inequality 25x+15y≥200

Question

, 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.

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

(20,11.5)

Answer 1

To determine whether the points (2, 3), (10, 10), and (20, 11.5) are viable solutions for the inequality \( 25x + 15y \geq 200 \), we can substitute each point into the inequality to see if it satisfies it.

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

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

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

In conclusion, the viable solutions among the points provided are (10, 10) and (20, 11.5). Thus, the correct answer to the question is:

(10, 10) is a viable solution in this context.