An electronic store makes a profit of $72 for every television sold and $90 for every computer sold. The managers target is to make at least $360 a day on sales from televisions and computers. Let x = the number of televisions sold. Let y = the number of computers sold. Which of the following represents three possible solutions to the problem?
A.) 72x + 90y >= 360
[A graph with points (0,4) and (5,0) as a line. Everything above is shaded]
(5,2) (3,3) and (1,4) are possible solutions
B.) 72x + 90y =< 360
[A graph with points (0,5) and (4,0) as a line. Everything below is shaded]
(4,0) (2,2) and (1,1) are possible solutions
C.) 72x + 90y >= 360
[A graph with points (0,4) and (5,0) as a line. Everything bellow is shaded]
(3,1) (2,2) and (1,0) are possible solutions
D.) 72x + 90y >= 360
[A graph with points (0,5) and (4,0) as a line. Everything above is shaded]
(4,0) (3,3) and (1,4) are possible solutions
I don't even know how to solve this... Please help?
the answer is a! the y intercept should be 4
option A
Step-by-step explanation:
Let x be the number of television sold and y be the number of computer sold
An electronics store makes a profit of $72 for every television sold and $90 for every computer sold.
Profit for x television is 72x
Profit of y computer is 90y
Total profit is 72x+90y sales profit is atleast 360
so inequality becomes 72×+90y >360 graph is attached below
(5,2) lies on the shaded part, so (5,2) is our solution
(3,3) lies on the shaded part, so (3,3) is our solution
(1,4) lies on the shaded part, so (1,4) is our solution (4,0) (2,2) (1,1) and (1,0) does not lies on the shaded part
So option A is correct
Yes, that is correct! The solution is represented by the shaded region above the line in option A. The y-intercept of the line should be (0,4) to indicate that the store needs to sell at least 4 televisions (with profit of $72 each) to make a profit of $360 or more.
Sure, I'd be happy to help! Let's break down the problem step by step.
First of all, let's examine the information given. The electronic store makes a profit of $72 for every television sold and $90 for every computer sold. The managers target is to make at least $360 a day on sales from televisions and computers.
To represent the problem mathematically, we can use two variables: x for the number of televisions sold and y for the number of computers sold.
The profit made from selling televisions would be given by 72x, and the profit made from selling computers would be given by 90y.
So, the total profit made from selling televisions and computers would be 72x + 90y.
The problem states that the managers' target is to make at least $360 a day on sales, so we can write this as an inequality: 72x + 90y >= 360.
Now, let's go through the given answer choices to find three possible solutions:
A.) 72x + 90y >= 360
This choice represents an inequality where the points (5,2), (3,3), and (1,4) lie above the line. These points satisfy the inequality, so they are possible solutions.
B.) 72x + 90y =< 360
This choice represents an inequality where the points (4,0), (2,2), and (1,1) lie below the line. These points do not satisfy the inequality, so they are not possible solutions.
C.) 72x + 90y >= 360
This choice represents an inequality where the points (3,1), (2,2), and (1,0) lie below the line. These points do not satisfy the inequality, so they are not possible solutions.
D.) 72x + 90y >= 360
This choice represents an inequality where the points (4,0), (3,3), and (1,4) lie above the line. These points satisfy the inequality, so they are possible solutions.
Therefore, the three possible solutions are (5,2), (3,3), and (1,4).
I hope this helps! Let me know if you have any more questions.
To solve this problem, you need to determine the inequalities that represent the conditions given in the question.
The first condition states that the store makes a profit of $72 for every television sold and $90 for every computer sold. Let x represent the number of televisions sold and y represent the number of computers sold. The total profit from televisions will be 72x, and the total profit from computers will be 90y.
The second condition states that the managers target is to make at least $360 a day on sales from televisions and computers. This means that the total profit from televisions and computers should be greater than or equal to $360. Therefore, the inequality representing this condition is:
72x + 90y >= 360
Now, let's check each option to see which of them represents three possible solutions to the problem:
Option A: The inequality is 72x + 90y >= 360. The graph represents a line passing through points (0, 4) and (5, 0), with everything above the line shaded. The possible solutions mentioned in the option are (5, 2) (3, 3) and (1, 4). These solution points do lie above the line, so option A is a possible solution.
Option B: The inequality is 72x + 90y <= 360. The graph represents a line passing through points (0, 5) and (4, 0), with everything below the line shaded. The possible solutions mentioned in the option are (4, 0) (2, 2), and (1, 1). These solution points do lie below the line, so option B is a possible solution.
Option C: The inequality is 72x + 90y >= 360. The graph represents a line passing through points (0, 4) and (5, 0), with everything below the line shaded. The possible solutions mentioned in the option are (3, 1) (2, 2), and (1, 0). These solution points do not lie below the line, so option C is not a possible solution.
Option D: The inequality is 72x + 90y >= 360. The graph represents a line passing through points (0, 5) and (4, 0), with everything above the line shaded. The possible solutions mentioned in the option are (4, 0) (3, 3), and (1, 4). These solution points do lie above the line, so option D is a possible solution.
Based on the analysis above, options A and B represent three possible solutions. Therefore, the correct answer is options A and B.
"at least $360" means ... ≥ $360
... B.) is eliminated
the solutions (shaded region) is above (greater than) the line
... C.) is eliminated
check the points for A.) and D.) to find the solution