Question
The graph shows the inequality 40x+30y≥1200
and represents Jake's earnings from washing cars and detailing, where x represents the number of cars washed and yy represents the number of cars detailed. Which of the labeled points is a viable solution in this context?
(1 point)
Responses
(-3,50)
(-3,50)
(15,25)
(15,25)
(10,20)
and represents Jake's earnings from washing cars and detailing, where x represents the number of cars washed and yy represents the number of cars detailed. Which of the labeled points is a viable solution in this context?
(1 point)
Responses
(-3,50)
(-3,50)
(15,25)
(15,25)
(10,20)
Answers
GPT-4o mini
To determine which of the labeled points is a viable solution for the inequality \( 40x + 30y \geq 1200 \), we can substitute the coordinates of each point into the inequality.
1. For the point \((-3, 50)\):
\[
40(-3) + 30(50) = -120 + 1500 = 1380
\]
Since \( 1380 \geq 1200 \), this point is a viable solution.
2. For the point \((15, 25)\):
\[
40(15) + 30(25) = 600 + 750 = 1350
\]
Since \( 1350 \geq 1200 \), this point is also a viable solution.
3. For the point \((10, 20)\):
\[
40(10) + 30(20) = 400 + 600 = 1000
\]
Since \( 1000 < 1200 \), this point is **not** a viable solution.
Thus, the viable solutions are \((-3, 50)\) and \((15, 25)\). If you are looking for just one point that meets the criteria, any of these two would be valid, but typically, we consider only points that are within the context of the problem (here, non-negative integers). Since \(-3\) is not a viable solution in realistic terms for the context of washing cars, \((15, 25)\) can be seen as the more appropriate viable solution.
1. For the point \((-3, 50)\):
\[
40(-3) + 30(50) = -120 + 1500 = 1380
\]
Since \( 1380 \geq 1200 \), this point is a viable solution.
2. For the point \((15, 25)\):
\[
40(15) + 30(25) = 600 + 750 = 1350
\]
Since \( 1350 \geq 1200 \), this point is also a viable solution.
3. For the point \((10, 20)\):
\[
40(10) + 30(20) = 400 + 600 = 1000
\]
Since \( 1000 < 1200 \), this point is **not** a viable solution.
Thus, the viable solutions are \((-3, 50)\) and \((15, 25)\). If you are looking for just one point that meets the criteria, any of these two would be valid, but typically, we consider only points that are within the context of the problem (here, non-negative integers). Since \(-3\) is not a viable solution in realistic terms for the context of washing cars, \((15, 25)\) can be seen as the more appropriate viable solution.