unit 1 – Alge
aic Thinking and Consumer Math
MATH 1001 – QUANTITATIVE REASONING
UNIT 1 – Alge
aic Thinking and Consumer Math
SECTIONS 6.2, 7.1
PROJECT: Snack Shop (Ratio, Proportion, and Percent)
Learning Goals
At the completion of the project, students will be able to:
• Compare unit ratios to determine the best buy.
• Solve problems using proportions.
• Identify the difference between Direct and Inverse Variation.
• Solve problems involving percents.
• Find percent increase or decrease.
Introduction
For business owners, math is a necessity. From ordering to selling products, business owners must use a
variety of mathematical processes to avoid waste and maximize profit. About 10% of Americans own
their own business. That may not sound like a lot, but here’s a far more interesting fact: 47% of people
with postgraduate degrees have a secondary source of income.
(https:
www.nbcnews.com
usiness
usiness-news/who-s-got-side-hustle-postgrads-people-earning-
80-000-n XXXXXXXXXXThis secondary source of income has recently taken on the name “side gig”. This
project will lead you through a fictional example of a side gig and explore many of the facets involved.
First, refer to sections 6.2 and 7.1 in your textbook. This project will utilize many of the topics covered
in those two sections. A set of terms follows.
A ratio is a comparison of two quantities using division.
A unit ratio is a ratio in which the denominator is 1. In order to calculate the unit ratio (also called unit
ate), perform the division of the ratio. One type of unit ratio you will use for this project is a Unit Price.
A proportion is an equation which states that two ratios are equal.
In direct variation, two quantities are related in such a way that if one goes up, the other goes up as
well or if one goes down, the other also goes down. However, sometimes quantities that are connected
vary so that if one goes up, the other goes down. This is called inverse variation.
A percent means hundredths, or per hundred. In this way, 1% = 1/100 = 0.01.
There are many applications using percents such as tax, commission, discount, markup, and percent
increase/decrease. One method for solving them is to use the basic proportion:
??????????????
100
=
????????
??ℎ??????
https:
www.nbcnews.com
usiness
usiness-news/who-s-got-side-hustle-postgrads-people-earning XXXXXXXXXXn1013621
https:
www.nbcnews.com
usiness
usiness-news/who-s-got-side-hustle-postgrads-people-earning XXXXXXXXXXn1013621
Page 2 of 4
UNIT 1 – ALGEBRAIC THINKING AND CONSUMER MATH
For each application, you would adjust the terms above as needed. For instance, to calculate tax:
??????????????
100
=
$ ??????
$ ???? ??????????
Example: What is the amount of tax charged for $63.45 of items with a tax rate of 8%? In this case, our
unknown is tax.
8
100
=
$ ??????
63.45
To solve this proportion, cross multiply (refer to example 4 in section 6.2 of the textbook). The amount
of tax is $5.076, which is rounded to $5.08. We can further extend our example by determining the total
amount we will pay for the items which will be $63.45 + $5.08 or $68.53.
Now, to explore some of the other applications.
1. Commission:
??????????????
100
= $ ????????????????????
$ ????????
2. Tip:
??????????????
100
= $ ??????
$ ???? ???????? ???????????? ??????
3. Discount:
??????????????
100
= $ ????????????????
???????????????? $ ???? ????????
4. Percent Increase/Decrease:
??????????????
100
= ???????????? ???? ????????????????/????????????????
???????????????? ????????????
When working with applications involving percent, there is often a second step to complete after solving
the proportions. In the tax example earlier, we saw that in order to find the total price it was necessary
to add the tax to the price of the goods. This is identical to thinking about Tip. The proportion given in
number 2 will calculate the amount of tip, but then that amount must be added to the price of the meal
to find the total amount. In Discount, we must do the opposite: subtract. In a way, we can think of Tip
and Tax as a Percent Increase (the amount is added), while Discount is a Percent Decrease (the amount
is subtracted).
Now, we will examine one further application of percent that we will use throughout this project,
Markup. The concept behind markup is that store owners must charge more than they pay for their
goods to earn a profit. There are a few different ways to calculate this amount, but for the purposes of
this project, we will use the method below:
Markup:
??????????????
100
= $ ????????????
??ℎ?????????????? $ ???? ??????????
Page 3 of 4
UNIT 1 – ALGEBRAIC THINKING AND CONSUMER MATH
First, the store owner chooses a percent. Then, they calculate the amount of the markup using the
given proportion. Finally, they add that markup amount to the wholesale cost of the goods to find the
price they will sell at.
Choosing the percent is a vital step in the process. The higher the percent, the higher the profit. Store
owners obviously want to make as much profit as possible, but they also don’t want to run buyers off by
charging too much. For more information, do a little research on the concept called the Law of Demand.
Background Information for Project
To earn some extra money, you have decided to open a snack shop on campus. You will purchase the
snacks to sell at wholesale prices and then sell at a higher price (price + markup) in order to make a
profit.
For the purpose of this project, we will assume the following relationships:
Markup Percent of Items sold
0-15% 100% of the items
16-40% 75% of the items
41-100% 50% of the items
To simplify things a little bit, we will assume that at the end of the semester you will be able to sell any
unsold items at cost in an everything-must-go sale. This means that unsold items will not affect your
profit.
We will also use the following choices of snacks and prices:
Wholesale snack prices via www.webstaurantstore.com
Salty Snacks Quantity Price per case
Lance Assorted Sandwich Crackers 1.4 oz. each/120 per case $22.77
Ritz Bitz Sandwich Crackers 1 oz./48 per case $20.43
Plain Potato Chips 1 oz./30 per case $9.00
Roasted and Salted Peanuts 1.5 oz./144 per case $75.55
Frito Lay Variety Pack Potato Chips 1 oz./60 per case $37.95
Sweet Snacks Quantity Price per case
Individually wrapped Muffins 2 oz./72 per case $20.01
Keebler Cookies 2 oz./60 per case $27.94
Nutri-Grain Bar 1.3 oz./48 per case $24.99
Famous Amos Cookies 2 oz./60 per case $27.94
Mars Assorted Candy Bars 1.7 oz./44 per case $38.29
Practice
Read through Sections 6.2 and 7.1 of the ebook. Pay special attention to Examples 4 and 6 in section 6.2
and Examples 1-7 in section 7.1. Work along with them and practice using your calculator to make sure
you are getting the same answers. Complete the “Try This One” problems, listed directly after each
Page 4 of 4
UNIT 1 – ALGEBRAIC THINKING AND CONSUMER MATH
suggested example. Notice you can quickly check your answer on these by hovering your mouse over
“Answer”.
Then complete the Unit 1 Homework Assignment in ALEKS. You have unlimited attempts on each
problem.
Learning Goals
Introduction
Background Information for Project
Practice
unit 2 – Financial Math PROJECT 2.2
Page 1 of 5
Name: _________________________
MATH 1001 – Section ___
Instructor: _____________________
Unit 1 Project: Snack Shop (Ratio, Proportion, Percent)
Instructions: Scan and submit all pages of this document to the appropriate Assignment folder in D2L.
With a budget of $250, you have decided to open a snack shop on campus. You can only choose 4 items to sell in your
shop (2 salty and 2 sweet). But, you can purchase multiple cases of each snack you choose. You must make sure to
purchase at least 500 items. This project will help you to decide which options will be best for your store. You will also
explore the potential profit you could make. Remember to refer to the background information given in the
instructions.
IMPORTANT: Round ALL dollar amounts at each step of the project to the nearest cent.
A. The first thing you will need to do is to compare the prices of the different items by calculating the Unit Price.
You will calculate both the price per item and the price per ounce to determine which snacks you want to
incorporate into your store.
Salty Snacks Cost per item Cost per ounce
Lance Assorted Sandwich Crackers
$0.19 $0.14
Ritz Bitz Sandwich Crackers
$0.43 $0.43
Plain Potato Chips
Roasted and Salted Peanuts
Frito Lay Variety Pack Potato Chips
Sweet Snacks Cost per item Cost per ounce
Individually wrapped Muffins
Keebler Cookies
Nutri-Grain Bar
Famous Amos Cookies
Mars Assorted Candy Bars
B. Now, you will decide the items and quantities you wish to purchase (two salty items and two sweet items).
Remember, your Budget is $250 and you must purchase at least 500 items to sell.
Page 2 of 5
Snack Name #Cases Total Cost Number of Items
Overall Cost and Number of Items
(**)
**Remember, the total price must be at or below $250 AND