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 (2,3) left parenthesis 2 comma 3 right parenthesis (10,10) left parenthesis 10 comma 10 right parenthesis (20,11.5) left parenthesis 20 comma 11.5 right parenthesis None of the points are a viable solution

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can substitute each of the given points into the inequality and check if it holds true.

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

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

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

From the checks:
- \( (2, 3) \) is not a viable solution.
- \( (10, 10) \) is a viable solution.
- \( (20, 11.5) \) is also a viable solution.

Since you asked for a viable solution and more than one point qualifies, you could simply state that any of the points \( (10, 10) \) or \( (20, 11.5) \) are viable solutions. If only one option must be selected, \( (10, 10) \) is a clear viable solution.

Thus, the answer is **(10, 10)**.