Question

This graph shows the inequality represents earnings 200x+15y= >= 200for 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)

(2,3)

Ο (20, 11.5)

None of the points are a viable solution

(10, 10)

Answer 1

To determine which of the labeled points is a viable solution to the inequality \(200x + 15y \geq 200\), we will evaluate each point in the context of the inequality.

1. **For the point (2, 3)**:
\[
200(2) + 15(3) = 400 + 45 = 445
\]
Since \(445 \geq 200\), this point is a viable solution.

2. **For the point (20, 11.5)**:
\[
200(20) + 15(11.5) = 4000 + 172.5 = 4172.5
\]
Since \(4172.5 \geq 200\), this point is also a viable solution.

3. **For the point (10, 10)**:
\[
200(10) + 15(10) = 2000 + 150 = 2150
\]
Since \(2150 \geq 200\), this point is also a viable solution.

Since all three points produce results that satisfy the inequality, the correct answer regarding viable solutions is:

- Both (2, 3), (20, 11.5), and (10, 10) are viable solutions; however, if only one point is to be selected from the options provided, the viable answer is (2, 3).

So depending on the context of the question, you could state that **(2, 3), (20, 11.5), and (10, 10) are all viable solutions**, or if strictly to choose one, you could mention **(2, 3)**.

If the question is limited to just one selection, then select **(2, 3)**.