Question

Use the image to answer the question. 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 (20,11.5) left parenthesis 20 comma 11.5 right parenthesis None of the points are a viable solution. None of the points are a viable solution. (2,3)

Answer 1

To determine which of the labeled points is a viable solution to the inequality $25x+15y\ge 200$, we will substitute each point into the inequality.

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

2. For the point $(20,11.5)$: $$25(20)+15(11.5)=500+172.5=672.5$$ Since $672.5\ge 200$, this point is also a viable solution.

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

Based on the checks, both $(10,10)$ and $(20,11.5)$ are viable solutions to the inequality. Therefore, if the question only asks for one viable solution from the provided choices, you can choose either $(10,10)$ or $(20,11.5)$.

If you need to pick only one based on the phrasing of the question, you can conclude with: (10, 10) as a viable solution.