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. (10, 10)
B. (2, 3)
C. None of the points are a viable solution
D. (20, 11.5)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we will plug each point into the inequality.

1. **Point A: (10, 10)**
\[
25(10) + 15(10) = 250 + 150 = 400
\]
Since \( 400 \geq 200 \), this point satisfies the inequality.

2. **Point B: (2, 3)**
\[
25(2) + 15(3) = 50 + 45 = 95
\]
Since \( 95 < 200 \), this point does not satisfy the inequality.

3. **Point D: (20, 11.5)**
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5
\]
Since \( 672.5 \geq 200 \), this point satisfies the inequality.

Now we summarize:

- Point A: (10, 10) is a viable solution.
- Point B: (2, 3) is not a viable solution.
- Point D: (20, 11.5) is a viable solution.

Since both points A and D are viable, but the options do not provide a choice for both, we can conclude that at least one point (A or D) is viable.

From the options provided, the answer would be:

**A. (10, 10)** is a viable solution, and is one of the correct answers.

However, since D (20, 11.5) is also a viable solution but was not listed in the choices, the best answer with the options is **C. None of the points are a viable solution**, cannot be chosen as there are viable points; hence the conclusion shows that A is the first valid answer.

The correct interpretation is therefore that **A. (10, 10)** is indeed a viable solution in the context!