Question 970916: In task three you found two ticket prices. (300 students = $8.50) (200 students = $9.75) Each price covers the cost of the dinner dance under certain conditions. Plan between 200 and 300 students, that is x > 200 and x < 300.
1) if your objective is to keep the ticket price as low as possible even at the risk of not covering your cost which ticket price would you select? Based on that choice right in the linear equation that gives the total amount collected for ticket sales. Change your equation to an inequality to indicate that this represents the least amount of money you expect to collect on ticket sales.
2). If your objective is to be sure that you cover the cost of the dinner dance which ticket price would you select? Based on the choice write linear equation that gives the total amount collected for ticket sales. Change your equation to an inequality to indicate that this represents the greatest amount of money you expect to collect on to ticket sales.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if 200 students show up, the cost will be 200 * 9.75 = 1950.
if 300 students show up, the cost will be 300 * 8.50 = 2550.
if you price the ticekts at 8.50 in order to keep the price low to attract more students, then your revenue will be less than or equal to 2550 and your equation would therefore be:
8.50 * x <= 2550.
x represents the number of students attending and 200 <= x <= 300.
if you price the tickets at 9.75 in order to make sure you have your costs covered, then your revenue will be greater than or equal to 1950 and your equation would therefore be:
9.75 * x >= 1950.
x represents the number of students attending and 200 <= x <= 300.
your cost equation can be calculated as follows:
you have 2 data points.
(200,1950)
(300,2550)
from these data points, you can determine that the cost equation will be y = 6x + 750.
first you find the slope which is 6.
then you find the y-intercept which is 750.
the slope is found by the formula (y2-y1)/(x2-x1) which becomes (2550-1950)/(300-200) which becomes 600/100 which becomes 6.
the y-intercept is found by y = 6x + b replacing y with 1950 and x with 200 to get 1950 = 6*200 + b and solving for b to get b = 750.
i didn't go through the details because i'm assuming you know how to create an equation from two points.
the crux of the issue is that the two points are (200,1950) and (300,255), where the x-values are the number of students attending and the y values are the total cost if that number of students attends.
your revenue equations for graphing are y = 8.50 * x and y = 9.75 * x.
your cost equation for graphing is y = 6x + 750.
your graph is shown below:
the blue line is the graph of y = 9.75x.
when you charge 9.75 per ticket, your revenue will greater than or equal to 1950.
you will be guaranteed to cover the cost of the affair, and will actually make more than the cost of the affair if more than 200 people show up.
the red line is the graph of y = 8.50x.
when you charge 8.50 per ticket, your revenue will be less than or equal to 2550.
if 300 people show up, you have covered your cost, but if less than 300 people show up, you have not covered the cost.
the cost of the affair is the black dashed line which is y = 6x + 750.
you can see that the blue line is greater than the cost of the affair when x is greater than 200.
you can see that the red line is less than the cost of the affair when x is less than 300.
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