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)
(2, 3)

(20, 11.5)
(20, 11.5)

(10, 10)
(10, 10)

None of the points are a viable solution.

Answer 1

To determine which labeled point is a viable solution to the inequality \( 25x + 15y \geq 200 \), we can test each point by substituting the values of \( x \) and \( y \) into the inequality.

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 does not satisfy the inequality.

2. For the point \( (20, 11.5) \): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] Since \( 672.5 \) is greater than \( 200 \), this point satisfies the inequality.

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

Thus, both \( (20, 11.5) \) and \( (10, 10) \) are viable solutions. However, the specific question asks for a labeled point, and since we've established that both satisfy the inequality, one valid response could be \( (20, 11.5) \) or \( (10, 10) \) based on the options.

Answer: \( (20, 11.5) \) or \( (10, 10) \) (as viable solutions).