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
(10,10)
left parenthesis 10 comma 10 right parenthesis
(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)
To determine which of the labeled points is a viable solution for the inequality 25x + 15y ≥ 200, we need to substitute the x and y values of each labeled point into the inequality and check if it holds true.
For the point (10, 10):
25(10) + 15(10) = 250 + 150 = 400
Since 400 is not greater than or equal to 200, the point (10, 10) is not a viable solution.
For the point (2, 3):
25(2) + 15(3) = 50 + 45 = 95
Since 95 is not greater than or equal to 200, the point (2, 3) is not a viable solution.
For the point (20, 11.5):
25(20) + 15(11.5) = 500 + 172.5 = 672.5
Since 672.5 is greater than or equal to 200, the point (20, 11.5) is a viable solution.
Therefore, the labeled point that is a viable solution in this context is (20, 11.5).