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 point is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can evaluate each of the points given:

1. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95 \quad (\text{not valid since } 95 < 200)
\]

2. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400 \quad (\text{valid since } 400 \geq 200)
\]

3. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5 \quad (\text{valid since } 672.5 \geq 200)
\]

Out of the choices provided, both (10, 10) and (20, 11.5) satisfy the inequality. However, since the question asks for which **labeled point** is a viable solution and does not query for multiple solutions, the most straightforward answer would be:

- **(10, 10)** is a viable solution.

Option: **(10, 10)**