Question

Use the image to answer the question.

The x- and y- axes of a coordinate plane range from 0 to 30 and 0 to 20 in increments of 5 and are labeled 'Lawns' and 'Dogs,' respectively. A line connects left parenthesis 0 comma 10 right parenthesis and left parenthesis 8 comma 0 right parenthesis.

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

(10,10)

left parenthesis 10 comma 10 right parenthesis
(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis
(2,3)
left parenthesis 2 comma 3 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 will test each point in the inequality.

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

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

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

Based on the calculations:
- The point \( (10, 10) \) satisfies the inequality.
- The point \( (20, 11.5) \) also satisfies the inequality.
- The point \( (2, 3) \) does **not** satisfy the inequality.

Since both \( (10, 10) \) and \( (20, 11.5) \) are viable solutions, but the question asks for one viable solution, you can choose either.

**Final Answer: (10, 10) or (20, 11.5) would be correct, but the response options seem limited based on your question.** If only one option can be marked and the instruction is to choose one, select one of the two that work (for example, \( (10, 10) \)).