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.

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?

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.

c. How much money will rent and utilities cost? Explain how you arrived at this answer.

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.

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) =
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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.

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.

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. Yesterday your store earned $797.30 just from the sale of cookies. Write and solve an equation that represents how many cookies were sold.

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.

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.

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 Cost Percentage
Labor $1,835
Materials 18%
Rent and utilities 25%
Miscellaneous $1,015
Total $5,000 100%

a. What percentage of the total monthly budget is spent on labor?

b. What percentage of the total monthly budget is spent on miscellaneous items?

c. How much do materials cost monthly?

d. How much do rent and utilities cost monthly?

How would you like us to help you with this assignment?

Please note that we have no access to the materials of any school, including Axia.

a 36.7%

b 20.3%
c $900
d $1250

To answer the questions in the activity, you will need to use mathematical equations and expressions. Follow the instructions for each question and use the given information to calculate the answers. Let's go through each question step by step:

1a. To represent your total budget, you need to add the loan amounts. Use the equation:
Total budget = $80,000 + $38,250

1b. To determine how much money will be spent on business space and utilities, you need to find 25% of your total budget. Write the algebraic expression:
0.25 * Total budget

1c. To calculate the actual cost of rent and utilities, substitute the value of the total budget into the expression from 1b and solve:
Rent and utilities cost = 0.25 * ( $80,000 + $38,250 )

1d. To determine if the investor's contribution is enough to meet the cost of rent and utilities, compare the additional amount to the cost. Write the inequality:
Investor's contribution >= ( Rent and utilities cost - Total budget )

1e. To calculate the remaining funds after paying for rent and utilities, subtract the cost from the total budget. Use the equation:
Remaining funds = Total budget - Rent and utilities cost

2. To calculate the temperature of the oven after a given amount of time, you need to determine the increase in temperature per minute and add it to the initial temperature. Write the expression:
Oven temperature = 70°F + ( 45°F / minute * 7 minutes )

3a. To find the total cost of all baked goods, multiply the cost of each item by the number of items. Write the expression:
Total cost = (2 * scones + 2 * cookies) + (1 * scones + 10 * cookies)

3b. To calculate the total revenue from selling all the baked goods, multiply the price of each item by the quantity. Use the equation:
Total revenue = (2.28 * scones + 1.19 * cookies) * (2 + 2 + 1)

3c. To find the number of cookies sold based on the given revenue, divide the total revenue by the price per cookie. Write the equation:
Total revenue from cookies = $797.30
Number of cookies sold = Total revenue from cookies / Price of a cookie

4a. To solve the profit formula for the cost, rearrange the equation:
Cost = Revenue - Profit

4b. To find the revenue given the profit and cost, add the cost to the profit. Use the equation:
Revenue = Profit + Cost

5a. To calculate the percentage of the total monthly budget spent on labor, divide the labor cost by the total budget and multiply by 100. Use the equation:
Labor percentage = (Labor cost / Total budget) * 100

5b. To calculate the percentage of the total monthly budget spent on miscellaneous items, divide the miscellaneous cost by the total budget and multiply by 100. Use the equation:
Miscellaneous percentage = (Miscellaneous cost / Total budget) * 100

5c. To find the monthly cost of materials, multiply the percentage by the total budget and divide by 100. Use the equation:
Materials cost = (Material percentage / 100) * Total budget

5d. To find the monthly cost of rent and utilities, multiply the percentage by the total budget and divide by 100. Use the equation:
Rent and utilities cost = (Rent and utilities percentage / 100) * Total budget

Remember to show your work and explain how you arrived at each answer.