Use the image to answer the 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(20,11.5)left parenthesis 20 comma 11.5 right parenthesis(10,10)left parenthesis 10 comma 10 right parenthesis(2,3)left parenthesis 2 comma 3 right parenthesisNone of the points are a viable solution.None of the points are a viable solution.Skip to navigation
To determine which of the labeled points is a viable solution, we need to substitute the values of x and y into the inequality and check if it is satisfied.
Let's check each point:
1) (20,11.5)
Substituting x = 20 and y = 11.5 into the inequality:
25(20) + 15(11.5) ≥ 200
500 + 172.5 ≥ 200
672.5 ≥ 200
Since 672.5 is greater than 200, this point is a viable solution.
2) (10,10)
Substituting x = 10 and y = 10 into the inequality:
25(10) + 15(10) ≥ 200
250 + 150 ≥ 200
400 ≥ 200
Since 400 is greater than 200, this point is a viable solution.
3) (2,3)
Substituting x = 2 and y = 3 into the inequality:
25(2) + 15(3) ≥ 200
50 + 45 ≥ 200
95 ≥ 200
Since 95 is not greater than or equal to 200, this point is not a viable solution.
Therefore, the viable solutions are (20,11.5) and (10,10). The correct answer is:
(20,11.5)