Question

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 point) Responses None of the points are a viable solution. None of the points are a viable solution. (2, 3) (2, 3) (10, 10) (10, 10) (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 the \(x\) and \(y\) values of each point into the equation and check if the inequality holds true.

1. For point (2, 3): \[ 25(2) + 15(3) = 50 + 45 = 95 \] \(95 \geq 200\) is false.

2. For point (10, 10): \[ 25(10) + 15(10) = 250 + 150 = 400 \] \(400 \geq 200\) is true.

3. For point (20, 11.5): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] \(672.5 \geq 200\) is also true.

Now we can evaluate the options:

• (2, 3) is not a viable solution.
• (10, 10) is a viable solution.
• (20, 11.5) is also a viable solution.

Therefore, both points (10, 10) and (20, 11.5) are viable solutions. However, if the question asks for just one viable solution and only includes the labelling of the points, then the response should include (10, 10), as it was the first viable point listed.

If the question specifies to select one point, the best response would be (10, 10).