Axia College Material
Appendix C
Starting a Business
Starting your own business can be exciting and daunting at the same time. Businesses use math when
managing finances, determining production levels, designing products and packaging, and monitoring
labor. A bakery can be a highly profitable and rewarding business. During this activity, you will apply the
skills from Ch. 1 & 2 to navigate some of the issues facing bakery owners.
Initial Budget:
$80,000 loan from family
$38,250 small business loan from bank
All loans to be repaid in 10 years
Application Practice
Answer the following questions. Use Equation Editor when writing mathematical expressions or
equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white
space below each question to maintain proper formatting.
1. You have recently found a location for your bakery and have begun implementing the first phases of
your business plan. Your budget consists of an $80,000 loan from your family and a $38,250 small
business loan. These loans must be repaid in full within 10 years.
a. What integer would represent your total budget?
80000 + 38250 = 118250
b. You will use 25% of your budget to rent business space and pay for utilities. Write an algebraic
expression that indicates how much money will be spent on business space and utilities. Do not
solve.
0.25 * 118250
c.
How much money will rent and utilities cost? Explain how you arrived at this answer.
I multiplied my budget by 0.25 and got 29562.50
d. Imagine an investor has increased your budget by $22,250. The investor does not need to be
repaid. Rather, he becomes part owner of your business. Will the investor contribute enough
money to meet the cost of rent and utilities? Support your answer and write an equation or
inequality that illustrates your answer.
It won’t cover the cost.
29562.50 > 22,250
MAT/116
e. This equation illustrates your remaining funds after paying for rent and utilities. How much money
is left? Explain how you arrived at your answer.
$38,250 + $80,000+ $22,250-0.25($80,000 + $38,250) =
140500 − 29562.50 = 𝟏𝟏𝟎𝟗𝟑𝟕. 𝟓𝟎
I started by adding the original investments. Then I multiplied by .25 to get the amount spent on
rent and utilities. Then I added up all the total investments, including from the new investor. Then
I subtracted the smaller amount from the larger.
2. You are trying to decide how to most efficiently use your oven. You do not want the oven running at a
high temperature when you are not baking, but you also do not want to waste a lot of time waiting for
the oven to reach the desired baking temperature.
The instruction manual on the industrial oven suggests the oven temperature will increase by 45
degrees Fahrenheit per minute. When the oven is initially turned on, the temperature is 70 degrees
Fahrenheit. What will the temperature of the oven be after 7 minutes? Write an expression and
explain how you arrived at your answer.
70 + (45 ∗ 7) = 70 + 315 = 385
I multiplied 45 degrees by 7 minutes and then added the result to the initial temperature of 70
degrees
3. In your industrial oven, you bake two baking sheets with 12 scones each, two baking sheets with 20
cookies each, and one baking sheet with 2 scones and 10 cookies.
a. Write an expression that illustrates the total cost of all baked goods in the scenario above using
the variable s to represent the cost of scones, and the variable c to represent the cost of cookies.
Simplify your expression by combining like terms.
𝐶 = (2 ∗ 12 ∗ 𝑠) + (2 ∗ 20 ∗ 𝑐) + 2𝑠 + 10𝑐
𝐶 = 26𝑠 + 50𝑐
b. Imagine you have decided to price the scones at $2.28 each and the cookies at $1.19 each. How
much total revenue would result from selling all the scones and cookies baked in the oven at one
time?
𝐶 = 26𝑠 + 50𝑐
𝐶 = 26(2.28) + 50(1.19)
𝐶 = 118.78
c.
Yesterday your store earned $797.30 just from the sale of cookies. Write and solve an equation
that represents how many cookies were sold.
1.19𝑐 = 797.30
𝑐 = 670
MAT/116
4. Your profit P is determined by subtracting the cost C, the amount of money it costs to operate a
business, from the revenue R, the amount of money you earn from selling your product. Profit can be
represented algebraically by the equations:
Profit = Revenue - Cost
OR
P=R-C
a. Rewrite the formula to solve for C.
𝐶 =𝑅−𝑃
b. Imagine your profit for 1 day is $1,281, and the cost of running the business for the day is $1,463.
What is the revenue for that day? Explain your answer.
𝑅 =𝐶+𝑃
𝑅 = 1463 + 1281
𝑅 = 2744
I converted the formula to solve for revenue. Revenue is costs plus profit (because profit is revenue
minus costs). I added together the profit and cost to get $2744.
5. When managing a business, it is important to take inventory of where your money is spent. You have
a monthly budget of $5,000. Refer to the table below and answer the questions that follow. Round
your answers to the nearest tenth of a percent.
Category
Labor
Materials
Rent and utilities
Miscellaneous
Total
Cost
Percentage
$1,835
18%
25%
$1,015
$5,000
100%
a. What percentage of the total monthly budget is spent on labor?
1835
= 0.367 = 36.7%
5000
b. What percentage of the total monthly budget is spent on miscellaneous items?
1015
= 0.203 = 20.3%
5000
c.
How much do materials cost monthly?
0.18 ∗ 5000 = $900
d. How much do rent and utilities cost monthly?
0.25 ∗ 5000 = $1250
MAT/116