# College Math 116 Week 2 Answer Guide- Algebra 1A -

### Algebra 1A

#### 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?

$118,250

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($118,250)

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

$29,562.50. Explanation: 0.25 is the decimal equivalent of 25%. The answer can be obtained by multiplying $118,250, the answer to part a, by 0.25.

d. Imagine an investor has increased your budget by $22,500. 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 costs of rent and utilities? Support your answer, and write an equation or inequality that illustrates your answer.

No, the investor did not contribute enough money to pay for the rent and utilities. These costs total $29,562.50 (answer to part c). Since $29,562.50>$22,500, the investor did not meet these needs.

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) = $110,937.50

#### 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 turned off, 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*x*

The oven will reach 385 degrees after 7 minutes. Substitute 7 for *x *in the expression. First, multiply 45 by 7 and then add 70.

3. Your industrial oven can bake two baking sheets with 12 scones each, two baking sheets with 20 cookies each, and one baking sheet with two scones and 10 cookies.

a. Write an expression that illustrates the scenario above using the variable *s *to represent scones, and the variable *c *to represent cookies. Simplify your expression by combining like terms.

2(12*s*) + 2(20*c*) + 2*s *+10*c*

This expression can be simplified to:

24*s *+ 40*c *+ 2*s *+10*c*, or 26*s *+ 50*c*

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?

26($2.28) + 50($1.19) = $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.

$1.19*c *= $797.30

*c *= 670

#### 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 equation:

**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 was the revenue for that day? Explain your answer.

$1,281 = *R *- $1,463

*R *= $2,744. By substituting $1,281 for *P *and $1,463 for *C*, the equation can be solved by adding $1,463 to $1,281.

#### 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?

36.7% of the total monthly budget is spent on labor.

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

20.3% of the total monthly budget is spent on miscellaneous items.

c. How much do materials cost monthly?

Materials for the month cost $900.

d. How much do rent and utilities cost monthly?

Monthly rent and utilities cost $1,250.