Question
The graph shows the inequality 40x+30y≥1200
.
This inequality represents Jake's earnings from washing cars and detailing, where x
represents the number of cars washed and y
represents the number of cars detailed.
Which of the labeled points is a viable solution in this context?
(1 point)
Responses
(15,25)
(15,25)
(10,20)
(10,20)
(10.5,30)
(10.5,30)
(-3,50)
(-3,50)
.
This inequality represents Jake's earnings from washing cars and detailing, where x
represents the number of cars washed and y
represents the number of cars detailed.
Which of the labeled points is a viable solution in this context?
(1 point)
Responses
(15,25)
(15,25)
(10,20)
(10,20)
(10.5,30)
(10.5,30)
(-3,50)
(-3,50)
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 each point into the inequality and check if it holds true.
1. For the point (15, 25):
\[
40(15) + 30(25) = 600 + 750 = 1350
\]
Since \( 1350 \geq 1200 \), this point is a solution.
2. For the point (10, 20):
\[
40(10) + 30(20) = 400 + 600 = 1000
\]
Since \( 1000 < 1200 \), this point is not a solution.
3. For the point (10.5, 30):
\[
40(10.5) + 30(30) = 420 + 900 = 1320
\]
Since \( 1320 \geq 1200 \), this point is also a solution.
4. For the point (-3, 50):
\[
40(-3) + 30(50) = -120 + 1500 = 1380
\]
Since \( 1380 \geq 1200 \), this point is a solution as well.
From the analyzed points, the viable solutions for the inequality are:
- (15, 25)
- (10.5, 30)
- (-3, 50)
However, it is important to remember that in the context of the problem (representing the number of cars washed and detailed), negative values such as (-3, 50) would not make logical sense, as you cannot wash a negative number of cars.
Thus, the viable solutions in the context of this problem are (15, 25) and (10.5, 30). The best answer that an expected context assumes (assuming non-negative quantities) would be (15, 25).
1. For the point (15, 25):
\[
40(15) + 30(25) = 600 + 750 = 1350
\]
Since \( 1350 \geq 1200 \), this point is a solution.
2. For the point (10, 20):
\[
40(10) + 30(20) = 400 + 600 = 1000
\]
Since \( 1000 < 1200 \), this point is not a solution.
3. For the point (10.5, 30):
\[
40(10.5) + 30(30) = 420 + 900 = 1320
\]
Since \( 1320 \geq 1200 \), this point is also a solution.
4. For the point (-3, 50):
\[
40(-3) + 30(50) = -120 + 1500 = 1380
\]
Since \( 1380 \geq 1200 \), this point is a solution as well.
From the analyzed points, the viable solutions for the inequality are:
- (15, 25)
- (10.5, 30)
- (-3, 50)
However, it is important to remember that in the context of the problem (representing the number of cars washed and detailed), negative values such as (-3, 50) would not make logical sense, as you cannot wash a negative number of cars.
Thus, the viable solutions in the context of this problem are (15, 25) and (10.5, 30). The best answer that an expected context assumes (assuming non-negative quantities) would be (15, 25).