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? A:(2,3) B: (10,10) C: none of the points are A variable solution D:(20,11.5) (choose one correct answer)
To determine which of the labeled points is a viable solution, we need to substitute the x and y values of each point into the inequality and see if the inequality is satisfied.
Let's test each point:
A: (2,3)
Substituting x = 2 and y = 3 into the inequality:
25x + 15y ≥ 200
25(2) + 15(3) ≥ 200
50 + 45 ≥ 200
95 ≥ 200
This inequality is not satisfied, so point A is not a viable solution.
B: (10,10)
Substituting x = 10 and y = 10 into the inequality:
25x + 15y ≥ 200
25(10) + 15(10) ≥ 200
250 + 150 ≥ 200
400 ≥ 200
This inequality is satisfied, so point B is a viable solution.
D: (20,11.5)
Substituting x = 20 and y = 11.5 into the inequality:
25x + 15y ≥ 200
25(20) + 15(11.5) ≥ 200
500 + 172.5 ≥ 200
672.5 ≥ 200
This inequality is satisfied, so point D is a viable solution.
Therefore, the labeled points that are viable solutions in this context are B: (10,10) and D: (20,11.5).
The correct answer is D.