Docstoc

AT THE CROSSROADS

Document Sample
AT THE CROSSROADS Powered By Docstoc
					Name:_____________________________________________________________ Period:________

                                       Valentine’s Day Fundraiser

The Harrison Prep ASB wants to sell roses for students to give to their friends and sweethearts on
Valentine’s Day to raise money for Senior Prom. They need to buy roses but want to get the best
price possible. So, they contacted several flower distributors and have narrowed the choice down to
two companies.




Option 1: Roses-R-Red has offered to sell its roses for a fixed down payment of $20.00 and an
additional charge of $0.75 per stem.

Option 2: The Flower Power has offered to sell its roses for a fixed down payment of $60.00 and
an additional charge of $0.50 per stem.

1. Predict which offer is the better deal. _______________________________________________

Explain why you made your choice: _________________________________________________

2. From the description of the two offers, complete the chart to find an algebraic rule that will
determine the cost of n roses.
                                             Rose Offers

                          Process                                    Process
                                               Cost at                                    Cost at
Number of Roses           Column                                     Column
                                             Roses-R-Red                               Flower Power
                       (Roses-R-Red)                             (Flower Power)
        10             20 + 10(0.75)            $27.50            60 + 10(0.50)            $65.00

        20
        40
        60
       120
       150
       210
       240
      1,000
        n
Name:_____________________________________________________________ Period:________


   a. Write a rule for the cost of roses at Roses-R-Red using words and symbols.

      1) Sentence using words: ____________________________________________________

      2) Sentence using symbols: ___________________________________________________

   b. Write a rule for the cost of roses at Flower Power using words and symbols.

      1) Sentence using words: ____________________________________________________

      2) Sentence using symbols: ___________________________________________________

   c. What patterns do you observe from the table of values? _______________________________

     ____________________________________________________________________________

   d. What happens to the cost of the roses as the number of roses purchased increases? _________

     ___________________________________________________________________________


   e. What would a graph of this relationship look like? ___________________________________

      ___________________________________________________________________________

   f. How many roses can you buy from Roses-R-Red for $65.00? __________________________
   Support your answer using words, numbers and/or diagrams.




   g. How many roses can you buy from Flower Power for $65.00? _________________________
   Support your answer using words, numbers and/or diagrams.




   h. What is the point where the two flower dealers charge the same amount? ________________

   i. Write an equation that represents the point where the two flower shops charge the same

   amount. _______________________________________________________________________
Name:_____________________________________________________________ Period:________



3. Graph the two functions on the same coordinate grid and label.
                  ___________________________________________________




4. What effect does the $0.75 per stem cost have on the graph of the Roses-R-Red function?

_________________________________________________________________________________

5. What effect does the $20.00 have on the graph? _______________________________________

_________________________________________________________________________________
Name:_____________________________________________________________ Period:________

6. What effect does the $0.50 per stem cost have on the graph of the Flower Power function?

_________________________________________________________________________________


7. What effect does the $60.00 have on the graph? _______________________________________

8. What is the significance of the point of intersection? ____________________________________

_________________________________________________________________________________

9. What is the point of intersection of the two graphs? _____________________________________
Show the work that supports your answer.




10. Which flower dealer offers the better deal and when? ___________________________________
Name:_____________________________________________________________ Period:________

                                        New Rose Offers




To entice potential new customers, Roses-R-Red decides to eliminate the $20.00 fixed charge.
According to its new offer, the ASB pays only for the roses they buy. When the Flower Power
learned about the new offer by its competitor, it immediately entered the price war by reducing its
$60.00 fixed charge to a $40.00 fixed charge.

1. How do the new offers compare to the original offers?    _________________________________

2. Make a prediction. Will it change which company has the better offer? _____________________
Support your prediction: ___________________________________________________________

3. From the description of each of the two new deals, complete the table and write new algebraic
rules that will determine the cost of n roses.

                                          New Rose Offers
   a.
                         Process                                    Process
Number of Roses                               Cost at                                    Cost at
                         Column                                     Column
                                            Roses-R-Red                               Flower Power
                      (Roses-R-Red)                             (Flower Power)
         10               10(0.75)              $7.50            40 + 10(0.50)            $45.00

         20

         40

         60

        120

        150

        210

        240

        1,000

         n
Name:_____________________________________________________________ Period:________


b. What patterns do you observe in the new table of values? ________________________________

_________________________________________________________________________________


c. Compare the costs in this table to the costs in the first table. What changes do you observe?

_________________________________________________________________________________

_________________________________________________________________________________




   d. How many roses can you buy from Roses-R-Red for $65.00? __________________________
   Support your answer using words, numbers and/or diagrams.




   e. How many roses can you buy from Flower Power for $65.00? _________________________
   Support your answer using words, numbers and/or diagrams.




   f. Write an equation that represents the point where the two flower shops charge the same
   amount.
   ______________________________________________________________________________

   g. At what point will the two flower dealers charge the same amount? ______________________

   What is the charge? __________________




   h. Which company offers the better deal?
Name:_____________________________________________________________ Period:________

                             Using Graphs for New Rose Offers
1. Graph both the original offer, y = 0.75x + 20, and the new offer, y = 0.75x, together.

       a. What effect does subtracting $20.00 from the old rule have on the new graph of the Roses-

       R-Red function? _____________________________________________________________

2. Turn off the above two graphs. Graph both the original offer, y = 0.5x + 60, and the new offer,
y = 0.5x + 40, together.

       a. What effect does subtracting $20.00 from the old rule have on the new graph of the Flower

       Power function? _____________________________________________________________

3. What are the coordinates of the point where the original two functions intersect? _____________

4. What are the coordinates of the point where two new functions intersect? ____________________

5. What is the significance of this point of intersection? ____________________________________

_________________________________________________________________________________

_________________________________________________________________________________

6. What affect did the new pricing structure have on the point of intersection? Why? ____________

_________________________________________________________________________________

_________________________________________________________________________________

7. Which flower dealer now offers the better deal? ________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________
Name:_____________________________________________________________ Period:________


8. Sketch the graphs of all four functions, label the graphs and label the relevant points of
intersection. Check your graphs on your graphing calculator. You may have to adjust your window
settings to see all your graphs.

				
DOCUMENT INFO
Categories:
Tags:
Stats:
views:5
posted:9/15/2011
language:English
pages:8