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 answer

To determine which labeled point is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can replace \( x \) and \( y \) in each point with the respective coordinates and check if they satisfy the inequality.

  1. Identify the coordinates of each labeled point on the graph.
  2. For each point, substitute the \( x \) and \( y \) values into the inequality \( 25x + 15y \).
  3. Check if the result is greater than or equal to 200.

Here are hypothetical examples of points for demonstration:

  • Point A: \( (4, 5) \)
  • Point B: \( (2, 8) \)
  • Point C: \( (6, 0) \)
  • Point D: \( (0, 10) \)

Let's calculate for each example:

  • Point A: \( 25(4) + 15(5) = 100 + 75 = 175 \) (not valid since \( 175 < 200 \))

  • Point B: \( 25(2) + 15(8) = 50 + 120 = 170 \) (not valid since \( 170 < 200 \))

  • Point C: \( 25(6) + 15(0) = 150 + 0 = 150 \) (not valid since \( 150 < 200 \))

  • Point D: \( 25(0) + 15(10) = 0 + 150 = 150 \) (not valid since \( 150 < 200 \))

You will need to plug in the actual coordinates of the labeled points from your graph to find out which point satisfies the inequality \( 25x + 15y \geq 200 \). If a point yields a result that is 200 or greater, then it is a viable solution within the context of Lina's earnings.

If you have specific labeled points, please provide them for precise calculations.