Intermediate Algebra II
Chapter 3 Project – Problem #2
Mr. Pardun
Name:
At next year’s Cougar 5K Classic, goodie bags will be available for purchase. The organizers of the event
have 600 protein bars, 500 water bottles, and 400 key chains, and they plan on packaging it in two
different bags; blue and silver. In the blue bag, there will be 2 protein bars, 1 water bottle, and 2 key
chains. In the silver bag, there will be 3 protein bars, 1 water bottle, and 1 key chain. The price of will
be $6.50 for the blue bag and $7.00 for the silver bag.
The organizers need you to determine how many of each bag should they put together in order to raise
the most money.
1. NUMBER OF BLUE BAGS (represented by the x variable)
a. Write an inequality that shows the number of blue bags can be 0 or larger.

1
2. NUMBER OF SILVER BAGS (represented by the y variable)
a. Write an inequality that shows the number of silver bags can be 0 or larger.

2
3. PROTEIN BARS
a. How many protein bars will be placed in the blue bag?
b. How many protein bars will be placed in the silver bag?
c. What is the total number of protein bars available?
d. Using x’s and y’s, write a linear inequality that shows how the protein bars will be
distributed to both bags.
3
+
 600
Teacher’s Initials:
4. WATER BOTTLES
a. How many water bottles will be placed in the blue bag?
b. How many water bottles will be placed in the silver bag?
c. What is the total number of water bottles available?
d. Using x’s and y’s, write a linear inequality that shows how the water bottles will be
distributed to both bags.
4
+

5. KEY CHAINS
a. How many key chains will be placed in the blue bag?
b. How many key chains will be placed in the silver bag?
c. What is the total number of key chains available?
d. Using x’s and y’s, write a linear inequality that shows how the key chains will be
distributed to both bags.
5
+

6. GRAPHING ON THE CALCULATOR
a. Put all 5 inequalities into the calculator and adjust your windows as shown below.
Xmin = -300
Xmax = 600
Xscl = 50
Ymin = -300
Ymax = 600
Yscl = 50
b. Use the TI Connect software to copy and paste your graph into this word document.
7. MAXIMIZING REVENUE
a. How much money is made from the sale of each blue bag ?
b. How much money is made from the sale of each silver bag?
c. Write an equation that represents the amount of revenue (R) the organizers will make by
selling x number of blue bags and y number of silver bags.
R=
+
d. Use the vertices from your graph to maximize the revenue equation above. Write your
ordered pair below along with the revenue it will generate.
e. How many of each bag should the organizers make for next year’s Cougar 5K Classic? How
much money will they make?