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

(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis

None of the points are a viable solution.
None of the points are a viable solution.

(10,10)
left parenthesis 10 comma 10 right parenthesis

Answer 1

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

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

2. **For the point \( (20, 11.5) \)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Check: \( 672.5 \geq 200 \) (True)

3. **For the point \( (10, 10) \)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Check: \( 400 \geq 200 \) (True)

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

Thus, both points \( (20, 11.5) \) and \( (10, 10) \) are viable solutions. However, if you need to select only one, then choose \( (20, 11.5) \), as it is a more extreme point in the context.

**Final Answer: \( (20, 11.5) \) is a viable solution.**