Question

This graph shows the inequality 25z +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)

(20,11.5)

(2,3)

None of the points are a viable solution

(10,10)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25z + 15y < 200 \), we need to substitute each point into the inequality and see if it satisfies it.

Let’s denote \( z \) (number of lawns mowed) as \( x \) and \( y \) as the number of dogs walked. So, we are checking the inequality \( 25x + 15y < 200 \).

### Checking each point:

1. **Point (20, 11.5)**:
\[
25(20) + 15(11.5) = 500 + 172.5 = 672.5 \, (not \, a \, solution)
\]

2. **Point (2, 3)**:
\[
25(2) + 15(3) = 50 + 45 = 95 \, (< 200 \, (is \, a \, solution))
\]

3. **Point (10, 10)**:
\[
25(10) + 15(10) = 250 + 150 = 400 \, (not \, a \, solution)
\]

### Conclusion:
The only point that satisfies the inequality \( 25z + 15y < 200 \) is **(2, 3)**. Thus, the viable solution in this context is **(2, 3)**.