This graph shows the inequality 25x+15y≥200

Question

25
𝑥
+
15
𝑦
≥
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

(10,10)
(
10
,
10
)
left parenthesis 10 comma 10 right parenthesis

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

(2,3)
(
2
,
3
)
left parenthesis 2 comma 3 right parenthesis

(20,11.5)

Answer 1

To determine which of the labeled points is a viable solution for the inequality \( 25x + 15y \geq 200 \), we can substitute the \(x\) and \(y\) values of each point into the inequality and see if it holds true.

1. For the point (10, 10): \[ 25(10) + 15(10) = 250 + 150 = 400 \] Since \( 400 \geq 200\), this point is a viable solution.

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

3. For the point (20, 11.5): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] Since \( 672.5 \geq 200\), this point is a viable solution.

Conclusion:

The viable solutions from the given points are (10, 10) and (20, 11.5). Therefore, both of these points are viable solutions. If you must select only one from the answers provided, (10, 10) is a correct choice. However, in context, there are also other viable solutions (like (20, 11.5)), but since it’s not listed as an option, the correct response in your context seems to be:

(10, 10).