All seasons Sports Ticket Worksheet
Name: _______________________
I. Refer the Family survey results and answer the following questions.
1. What do you expect to be the relationship between the price the students set for
the tickets and the response to the sale?
2. How can the class officers use this information to determine the "best" price for a
single ticket?
3. Imagine that you are in charge of the sale and it is your responsibility to
determine the price of the tickets. Where do you begin?
4. What information about the parents and their support for the sale is contained in
the data?
5. Do the data support the conjecture that the more the ticket costs, the fewer
families would be interested?
6. What are the dependent and independent variables in the data? How do you
know?
III. STEPS TO WORK ON FATHOM 2 ON YOUR COMPUTER:
 Open Fathom 2 on your computer and drag a new collection and add table to
the screen.
 Add the attributes Maximum Price and Expected ticket sales to the table and
then enter the data.
 On Fathom, drag the graph from the menu. Add the independent variable on
the horizontal axis of the graph and the dependent variable on the vertical
axis of the graph.
Answer the following questions based on your scatter plot.
7. Does the scatter plot provide with useful information?
8. Do you see any pattern?
9. Did all of the families respond to the survey question? If a family did not respond,
what does this mean about their interests in the tickets?
IV. According to the results of the survey, 150 families are willing to pay as much as
$175 for each ticket. How many families will be willing to pay $150 per ticket?
There are 60 families willing to pay up to $150, and families willing to pay $175 will
certainly be willing to pay $150 for each ticket. Therefore, we would expect 150 + 60
= 210 families to purchase tickets priced at $150.
10. Continuing to sum each successive number of ticket buyers, create new attribute
cumulative ticket sales on Fathom 2 in the existing table on the screen showing how
many families you can expect to purchase tickets at each price.
11. Construct the scatter plot using the attributes Maximum price and the
Cumulative ticket sales:
12. Does the graph show any useful information about the data?
13. What relationship do you notice between the ticket price and the number of
tickets the students can expect to sell?
On your Fathom screen, select the scatter plot and right click on the graph. A menu
will appear, select add least square line. This line will help you find the line of best
fit.
14. Write down the equation for the least square line from the graph. Explain its
meaning in context.
15. In the linear equation for the number of tickets sold, Cumulative_ticket_sales = 5.08*Maximum_price +1000, interpret the meaning of slope, the x-intercept and the
y-intercept. In this case, maximum price and the cumulative ticket sales.
16. If you charge $60.00 per ticket, how many tickets would you expect to sell? How
about if you sell at $110.00? or $185.00? (Hint: Hold the mouse on the leastsquare
line and once the red dot appears drag it on the line anywhere and notice the
ordered pair (price, ticket_sales) is displayed at the left hand corner at the bottom of
the screen)
V. Looking Back
17. What is your goal in your investigation?
18. Does the function Cumulative_ticket_sales = -5.08*Maximum_price +1000;
answer your goal? Why or why not?
19. If you multiply the ticket price with the number of tickets sold, what do you get?
What is it called?
20. Write the formula for revenue.
Go to your fathom screen and add the attribute “Revenue” in the existing table.
Open the inspector by double clicking on the collection and in the revenue row click
on the formula section and enter the formula for revenue.
22. What do you notice in the revenue column?
Drag the new graph from the fathom menu and drop it on the screen. Add the
attribute max_price and revenue respectively on the horizontal and the vertical axis.
23. What pattern do you see from the graph? How is it different from the graph
between maximum price and the cumulative ticket sales you did earlier?
24. a. What shape do you predict for the graph? why? b. Does the graph has a
maximum or minimum?
25. Describe the reasonable domain and range for the problem situation?
26. Describe the relationship between the revenue generated and the price of the
ticket?
INVESTIGATE:
Drag two sliders from the menu and drop it into your document. Rename them
‘a’ and ‘b’ by clicking on their names and typing new ones.
Select the graph and choose Plot Function from the Graph menu. Enter the
formula a .(maximum_price)2 + b. maximum_price in the formula editor. A
parabola should appear on the graph. Rescale graph axes from the Graph menu.
Adjust the ‘a’ slider and watch how the curve changes. (You may want to
change the bounds on the slider axis to bring negative numbers into view. Grab
the right end of the axis and drag right.)
27. Describe the way the curve changes when you change the value of ‘a’.
Adjust the ‘b’ slider. (Double click near the axis and enter new values for the
Lower and Upper bounds)
28. Describe how the curve changes when you change the value of ‘b’.
29. Move both sliders to fit the function to the data. (Hint: The values of a and b
have something to do with the least square function you have found) If your
function doesn’t fit the points, adjust the slider until it does.
30. What values of ‘a’ and ‘b’ fit the data best? How did you come to this
conclusion? Explain as clearly as you can what ‘a’ and ‘b’ represent.
31. What other way can you determine if the values of ‘a’ and ‘b’ are the best fit?
(Hint: what is the revenue function?)
32. What is the vertex of the parabola you found? (Recall that the vertex lies
midway between two zeros) Explain what it means in the problem situation.
Select the graph and choose plot value from the Graph menu and enter the vertex
you found. A vertical line (or line of symmetry) passes through the vertex. Hold the
cursor at the intersection of the parabola and the vertical line, a red dot appears and
the respective coordinates appear at the left hand corner at the bottom of the screen.
33. Explain in context what the coordinates represent in context of the problem.
34. What is the optimum price you would set for the ticket to collect the maximum
revenue?
35. How many tickets would you expect to sell at the optimum price?