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Math Help - Linear equation to Inequality problem

  1. #1
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    Linear equation to Inequality problem

    I've done all these sections already and am stuck on Part 4. The other parts are necessary though so you can figure out Part 4.

    Part 1
    Band A charges $600 to play for the evening. Band B charges $350 plus $1.25 for each ticket sold. Write a linear equation for the cost of each band. Graph each equation and find the number of tickets for which the cost of the two bands will be equal.
    Band A- C=0x + 600
    Band B- C=1.25x + 350
    At 200 tickets they would be equal

    Part 2
    A caterer charges a fixed cost for preparing dinner plus a cost for each person served. You know that the cost for 100 people will be $750 and the cost for 150 people will be $1050. Find the caterer's fixed cost and the cost per person served.
    1(750= 100x + y) 750= 100x + 1y
    -1(1050= 150x + y) -1050= -150x + -1y
    -300 = -50x
    /-50 /-50
    750=100(6) + y 6 = x
    750= 600 + y
    y= 150

    Fixed cost = $150
    Cost per student = $6

    Part 3
    Use your information from the first two sections of this project. Assume that 200 people will come to the dance. Write a report listing which band you would choose and the cost per ticket that you need to charge to cover expenses. Then repeat the process assuming that 300 people will come.



    200 students
    0(200) + 600 = 600 Band A
    1.25(200) + 350 = 600 Band B
    Catering:
    C= 200(6) + 150
    C= 1350
    1350 + 600 = 1950
    1950/200 = $9.75 per ticket

    300 students
    0(300) + 600 = 600 Band A
    1.25(300) + 350 = 725 Band B
    Catering:
    C= 300(6) + 150
    C= 1950
    1950 + 600 = 2250
    2250/300 = $8.50 per ticket

    Part 4


    In part 3 you found two ticket prices. Each price covers the cost of the dance under certain conditions. Decide what the ticket price should be. Plan for between 200 and 300 people.
    -If your objective is to keep the ticket price as low as possible, even at the risk of not covering your costs, which ticket price would you select? Based on this choice, write a 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 from ticket sales.

    Would it be
    C = 250(6.00)
    C ≤ 250 (6.00)
    Since you could pick any number between 200 and 300?

    -If your objective is to be sure that you are able to cover the cost of the dinner dance, which ticket price would you select? Based on this choice, write a 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 from ticket sales.

    __________________________________________________ __

    -The two inequalities you have written, along with x>200 and x<300, form a system of linear inequalities. Graph this system to show the total amount recieved from ticket sales

    __________________________________________________ __________

    Thank you,
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  2. #2
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    Hi, Bica!

    Quote Originally Posted by Bica View Post
    Part 3
    ...
    1950 + 600 = 2250
    2250/300 = $8.50 per ticket
    This should be 1950 + 600 = 2550, but I suppose that was a typo since 2550/300 is still 8.5.
    Quote Originally Posted by Bica View Post
    Part 4

    In part 3 you found two ticket prices. Each price covers the cost of the dance under certain conditions. Decide what the ticket price should be. Plan for between 200 and 300 people.
    -If your objective is to keep the ticket price as low as possible, even at the risk of not covering your costs, which ticket price would you select? Based on this choice, write a 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 from ticket sales.

    Would it be
    C = 250(6.00)
    C ≤ 250 (6.00)
    Since you could pick any number between 200 and 300?
    Well, if you want to make the price as low as possible, assume that the minimum number of people will show up (200) and base your price off of that. So, if C is the amount of money we collect, then at minimum we would get 200\cdot6.00 = 1200, and we have

    C\geq\$1200

    Quote Originally Posted by Bica View Post
    -If your objective is to be sure that you are able to cover the cost of the dinner dance, which ticket price would you select? Based on this choice, write a 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 from ticket sales.
    This time, we want to plan for the maximum number of people (300) so that we can be sure to cover our cost no matter what. I assume that that last sentence should read "this represents the greatest amount of money you expect to collect," and so we have

    C\leq\$300\cdot8.5=\$2550

    and

    \$1200\leq C\leq\$2550

    Can you graph this?
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