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. (20, 11.5)
B. None of the points are a viable solution.
C. (2, 3)
D. (10, 10)
To determine which point is a viable solution, we need to substitute the coordinates of each point into the inequality and see if it is true.
Let's substitute the coordinates of point A (20, 11.5) into the inequality:
25x + 15y ≥ 200
25(20) + 15(11.5) ≥ 200
500 + 172.5 ≥ 200
672.5 ≥ 200
Since 672.5 is greater than 200, this point satisfies the inequality.
Now let's substitute the coordinates of point C (2, 3) into the inequality:
25x + 15y ≥ 200
25(2) + 15(3) ≥ 200
50 + 45 ≥ 200
95 ≥ 200
Since 95 is not greater than 200, this point does not satisfy the inequality.
Finally, let's substitute the coordinates of point D (10, 10) into the inequality:
25x + 15y ≥ 200
25(10) + 15(10) ≥ 200
250 + 150 ≥ 200
400 ≥ 200
Since 400 is greater than 200, this point satisfies the inequality.
Therefore, the viable solution in this context is option D, which is (10, 10).