Use the image to answer the question.

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, \( (10, 10) \)).