Document Sample

```					Name:_____________________________________________________________ Period:________

Valentine’s Day Fundraiser

The Harrison Prep ASB wants to sell roses for students to give to their friends and sweethearts on
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. _______________________________________________

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? __________________________

g. How many roses can you buy from Flower Power for \$65.00? _________________________

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? _____________________________________

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? _____________________

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? __________________________

e. How many roses can you buy from Flower Power for \$65.00? _________________________

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