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) Twenty-five percent of your budget will be used 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) Suppose 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) =
¬
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 it is 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 your oven temperature will increase by 45 degrees Fahrenheit per minute. When the over 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) Suppose 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) Suppose your profit for one 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/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?
a) The integer that represents the total budget is $80,000 + $38,250 = $118,250.
b) The algebraic expression that indicates how much money will be spent on business space and utilities is 0.25(total budget).
c) The money spent on rent and utilities can be found by substituting the total budget into the expression from part b: 0.25($118,250) = $29,562.50. This is the cost of rent and utilities.
d) After the investor contributes an additional $22,250, the new total budget becomes $118,250 + $22,250 = $140,500. To check if this amount is enough to cover the cost of rent and utilities, we can compare it to the cost calculated in part c. The inequality would be: $140,500 ≥ $29,562.50.
e) To find the remaining funds, we subtract the cost of rent and utilities from the new total budget: $140,500 - $29,562.50 = $110,937.50. This is the amount of money left after paying for rent and utilities.
2. The expression that represents the temperature of the oven after 7 minutes can be found by adding 45 degrees Fahrenheit per minute for 7 minutes to the initial temperature of 70 degrees Fahrenheit: 7(45) + 70 = 355 degrees Fahrenheit. The temperature of the oven after 7 minutes will be 355 degrees Fahrenheit.
3. a) The expression that illustrates the total cost of all baked goods can be found by multiplying the number of each item by its respective cost and then summing all the costs:
2(12s) + 2(20c) + (2s + 10c) = 24s + 40c + 2s + 10c = 26s + 50c.
b) Since scones are priced at $2.28 each and there are 26 scones, the cost of scones is 26 * $2.28 = $59.28. And since cookies are priced at $1.19 each and there are 50 cookies, the cost of cookies is 50 * $1.19 = $59.50. The total revenue from selling all the scones and cookies baked in the oven at one time would be $59.28 + $59.50 = $118.78.
c) To find the number of cookies sold based on the revenue of $797.30, we divide the revenue by the price per cookie: $797.30 / $1.19 = 670 cookies were sold.
4. a) To solve for C in the formula P = R - C, we can rearrange the formula to C = R - P.
b) Since the profit for the day is $1,281 and the cost of running the business for the day is $1,463, we can substitute these values into the formula from part a to solve for the revenue: R = C + P = $1,463 + $1,281 = $2,744. The revenue for that day is $2,744.
5. a) The percentage of the total monthly budget spent on labor is ($1,835 / $5,000) * 100% = 36.7%.
b) The percentage of the total monthly budget spent on miscellaneous items is ($1,015 / $5,000) * 100% = 20.3%.
c) The cost of materials can be found by multiplying the total budget by the percentage allocated to materials: ($5,000 * 18%) = $900.
d) The cost of rent and utilities can be found by multiplying the total budget by the percentage allocated to rent/utilities: ($5,000 * 25%) = $1250.
1a) The integer that represents your total budget is the sum of the two loans, which is $80,000 + $38,250 = $118,250.
b) To write an algebraic expression that indicates how much money will be spent on business space and utilities, we need to find 25% of the total budget. Let's call the total budget B. The expression would be: 0.25 * B.
c) To find out how much money will be spent on rent and utilities, we need to substitute the total budget B into the expression 0.25 * B. The calculation would be: 0.25 * ($118,250) = $29,562.50. Therefore, the rent and utilities will cost $29,562.50.
d) If the investor has increased the budget by $22,250, the new budget would be the sum of the total budget and the additional amount: $118,250 + $22,250 = $140,500. To determine whether this is enough to cover the cost of rent and utilities, we need to compare it to the cost. We can write an inequality to represent this: Budget ≥ cost. Substituting the values, the inequality would be: $140,500 ≥ $29,562.50. Therefore, the investor's contribution is enough to meet the cost of rent and utilities.
e) The equation provided, $38,250 + $80,000 + $22,250 - 0.25 * ($80,000 + $38,250) = remaining funds. We can simplify the equation: $140,500 - 0.25 * ($118,250) = remaining funds. Calculating this, we get $140,500 - $29,562.50 = $110,937.50. Therefore, there will be $110,937.50 left after paying for rent and utilities.
2) The initial temperature of the oven is 70 degrees Fahrenheit, and it increases by 45 degrees Fahrenheit per minute. To find the temperature after 7 minutes, we can multiply the rate of increase (45 degrees/minute) by the number of minutes (7). The expression for the temperature after 7 minutes is: 70 + (45 * 7) = 385 degrees Fahrenheit.
3a) The expression that illustrates the total cost of all baked goods is: (2 * 12s + 2 * 20c) + (2s + 10c), where s represents the cost of scones and c represents the cost of cookies. Simplifying this expression, we get: 24s + 40c + 2s + 10c = 26s + 50c.
b) If we price the scones at $2.28 each and the cookies at $1.19 each, we can calculate the total revenue by substituting the prices into the simplified expression: 26 * $2.28 + 50 * $1.19 = $59.28 + $59.50 = $118.78. Therefore, the total revenue would be $118.78.
c) Let's represent the number of cookies sold as x. If the revenue from the sale of cookies is $797.30, we can write the equation: $1.19x = $797.30. Solving for x, we divide both sides by $1.19: x = $797.30 / $1.19 = 670.59. Therefore, approximately 671 cookies were sold.
4a) To solve for C in the formula P = R - C, we need to isolate C. First, let's subtract P from both sides of the equation: P - R = -C. Then, multiply both sides by -1 to change the sign of the equation: C = R - P. Therefore, the formula to solve for C is C = R - P.
b) If the profit for one day is $1,281 and the cost of running the business for the day is $1,463, we can use the formula P = R - C to find the revenue. Rearranging the formula, R = P + C, we substitute the values: R = $1,281 + $1,463 = $2,744. Therefore, the revenue for that day is $2,744.
5a) To find the percentage of the total monthly budget spent on labor, we divide the cost of labor ($1,835) by the total budget ($5,000) and then multiply by 100: ($1,835 / $5,000) * 100 = 36.7%. Therefore, 36.7% of the total monthly budget is spent on labor.
b) To find the percentage of the total monthly budget spent on miscellaneous items, we divide the cost of miscellaneous items ($1,015) by the total budget ($5,000) and then multiply by 100: ($1,015 / $5,000) * 100 = 20.3%. Therefore, 20.3% of the total monthly budget is spent on miscellaneous items.
c) The materials cost is given as 18% of the total monthly budget, so we can calculate it by multiplying the total budget ($5,000) by 0.18: $5,000 * 0.18 = $900. Therefore, the materials cost monthly is $900.
d) The rent and utilities cost is given as 25% of the total monthly budget, so we can calculate it by multiplying the total budget ($5,000) by 0.25: $5,000 * 0.25 = $1,250. Therefore, the rent and utilities cost monthly is $1,250.