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 to the inequality \( 25x + 15y \geq 200 \), we can substitute each point into the inequality and see if it holds true.

1. For the point \((2, 3)\):
\[
25(2) + 15(3) = 50 + 45 = 95
\]
\[
95 \geq 200 \quad \text{(False)}
\]

2. For the point \((10, 10)\):
\[
25(10) + 15(10) = 250 + 150 = 400
\]
\[
400 \geq 200 \quad \text{(True)}
\]

3. For the point \((20, 11.5)\):
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
\[
672.5 \geq 200 \quad \text{(True)}
\]

Now we can summarize the results:
- \((2, 3)\) is not a viable solution.
- \((10, 10)\) is a viable solution.
- \((20, 11.5)\) is also a viable solution.

Therefore, the labels \((10, 10)\) and \((20, 11.5)\) are both viable solutions. If the question asks for one viable solution, then either can be accepted.

So, the answer is \((10, 10)\) as a viable solution.