Use the image to answer the question.

Question

The x- and y- axes of a coordinate plane range from 0 to 30 and 0 to 20 in increments of 5 and are labeled 'Lawns' and 'Dogs,' respectively. A line connects left parenthesis 0 comma 10 right parenthesis and left parenthesis 8 comma 0 right parenthesis.

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

None of the points are a viable solution.
None of the points are a viable solution.

(20,11.5)
left parenthesis 20 comma 11.5 right parenthesis

(10,10)

Answer 1

To determine which labeled point is a viable solution for Lina’s earnings represented by the inequality \( 25x + 15y \geq 200 \), we will substitute each of the given points into the inequality and check if they satisfy it.

1. Point (2, 3):

   • Substitute \( x = 2 \) and \( y = 3 \): \[ 25(2) + 15(3) = 50 + 45 = 95 \]
   • Check: \( 95 \geq 200 \) (False)

2. Point (20, 11.5):

   • Substitute \( x = 20 \) and \( y = 11.5 \): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \]
   • Check: \( 672.5 \geq 200 \) (True)

3. Point (10, 10):

   • Substitute \( x = 10 \) and \( y = 10 \): \[ 25(10) + 15(10) = 250 + 150 = 400 \]
   • Check: \( 400 \geq 200 \) (True)

After evaluating all points:

• (2, 3) is not a viable solution.
• (20, 11.5) is a viable solution.
• (10, 10) is a viable solution.

Conclusion: The labeled point (20, 11.5) is a viable solution for the inequality \( 25x + 15y \geq 200 \).