Solving Inequalities Unit Portfolio ALGEBRA 1 A
Directions: Complete each of the tasks outlined below.
Task 1
You want to start a summer business to earn money. What will you do? You have to
consider how much money you can afford to invest in this business, how much it
will cost you to make each item, and how much you’re going to charge for each
item. Research something that would be reasonable to make and sell with the startup investment you have determined.
a. What is the total amount of money you are willing to invest in this business?
b. What item are you going to make and sell? Why?
c. Describe how your business will work. How much will it cost you to make
each item? How much will you sell each item for?
d. Do you think your business will be profitable? Explain your answer.
Task 2
In Task 1 you determined how much of your own money you’re willing to spend to
get your business started. This is your limit—when making your product you can’t
exceed this amount.
a. Write an inequality that represents the fact that while making your product
you can’t exceed this spending limit.
b. Solve this inequality and graph the solution on a number line. Explain what
your solution means in terms of the situation.
c. In Task 1 you determined how much you will charge for each item. Write an
equation that represents your total earnings based on the price of your item
and how many you sell.
d. Using your answer from part B and your equation from part C, what is the
most money you can hope to earn from your business?
e. Don’t forget that at the beginning of the process you had to spend some of
your own money to get started. With the costs taken into account, what was
your total profit? Did you make money or lose money? Now that you have
these values, would you adjust your business plan from Task 1? If so, how?
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Task 3
Your parents heard about the success of your business and they want to help you
out. Suppose they want to give you an additional $300 to put toward your business.
However, there’s a catch. If you make more than $600 total, you have to give them
10% of your earnings above $600. For example, if you have earned $650, then you
owe 10% of $50, or $5, to your parents.
a. Now that you have an additional $300, revise your inequality from part A of
Task 2 to reflect your new spending limit. Solve this inequality and graph the
solution on a number line. Explain what your solution means in terms of the
situation.
b. If you still sell your item for the same price, what is the most money you can
hope to earn from your business now?
c. Will you have to pay your parents? If so, determine how much you will owe
them.
d. Think about how much time it will take you to create your product. You have
200 hours this summer to devote to creating your product. Write an
inequality that represents your time constraint.
e. Solve your inequality from part D and graph your solution on a number line.
Explain what your solution means in terms of the situation.
f. With the costs taken into account, what was your total profit? Did you make
or lose money? Now that you have these values, would you adjust your
business plan from Task 1? If so, how?