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?
A. no
B. (20, 11.5)
C. (2, 3)
D. (10, 10)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \(25x + 15y \geq 200\), we need to evaluate each option by substituting the coordinates into the inequality.

1. **Point A**: No (not applicable for numerical check)

2. **Point B (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \(672.5 \geq 200\), this point is a viable solution.

3. **Point C (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \(95 < 200\), this point is not a viable solution.

4. **Point D (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \(400 \geq 200\), this point is also a viable solution.

Both points B and D satisfy the inequality. However, since you are looking for a single viable solution from the provided options:

The answer is **B. (20, 11.5)**.