This graph shows the inequality 25 + 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?

Question

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

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25 + 15y > 200 \), we first need to simplify the inequality and isolate \( y \):

1. Start with \( 25 + 15y > 200 \).
2. Subtract 25 from both sides: \( 15y > 175 \).
3. Divide by 15: \( y > \frac{175}{15} \).
4. Simplifying \( \frac{175}{15} \) gives us \( y > 11.67 \).

Now, we can evaluate the provided points:

1. Point (2, 3): Here \( y = 3 \).

   • \( 3 \) is not greater than \( 11.67 \) → Not a viable solution.

2. Point (20, 11.5): Here \( y = 11.5 \).

   • \( 11.5 \) is not greater than \( 11.67 \) → Not a viable solution.

3. Point (10, 10): Here \( y = 10 \).

   • \( 10 \) is not greater than \( 11.67 \) → Not a viable solution.

Since we find that none of the points provided satisfy the inequality \( y > 11.67 \), the result is:

None of the points are a viable solution.