Solving Linear Equations

Please see the attached file for the fully formatted problems.

1. Solve . You must show all work to receive full credit.

Show work here:

Final answer:

2. Solve . You must show all work to receive full credit.

Show work here:

Final answer:

3. A real estate broker's base annual salary is $18,000. She earns 3% commission on
total sales. How much must she sell in real estate value during the year to earn
$65,000? Set up an equation and solve. Show all work to receive full credit. Round
final answer to the nearest dollar.

Equation:

Show work here:

Final answer:

4. The equation represents the formula for total distance traveled. The distance
traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use this
formula to help solve the following problem.

Tina and Tim work together and are planning to take a trip this weekend. On Friday afternoon, Tina gets a head start and leaves work in her car traveling at 45 mph. Three hours later, Tim leaves work on the same road at 65 mph. Assuming there is no traffic, in how many hours will Tim pass Tina?

A. Who will be driving longer and by how much?
Answer:

B. Once Tim catches up with Tina, who will have gone the farther distance?
Answer:

C. What equation represents this situation?
Answer:

D. Solve the equation; show your work here:
Answer:

E. How many hours did it take Tim to pass Tina?
Answer:

5. Solve the following two equations separately: and

Show work for solving here:

Show work for solving here:

Explain the difference between the two solutions; explanation must be detailed to receive full credit:
Answer:

6. A grocery store may increase the original price of a product to cover the expenses of running the store. The markup is the amount that is added to the original cost to create the selling price (the price the consumer pays) of the groceries. The percent markup is called the markup rate and is usually expressed as a percent of the original price. Taking the original cost and adding the markup calculates the selling price of an item. The formula can be used to help find the selling price. The selling price, S, is equal to the original cost, C, plus the markup rate, r, multiplied by the original cost, C (Aufmann, Vernon, & Lockwood, 2006).

Using the aforementioned information, solve the following problems.

A. A carton of eggs originally costs the store $0.98, but to make money, the store wants to have an 85% markup on the carton of eggs. Use the selling price formula to find the new price of the eggs. Round to the nearest cent.

Set up equation:

Show work here:

Selling price of eggs:

B. A 20-lb turkey has a 35% markup and is selling for a price of $22.50. Use the selling price formula to find the original cost of the turkey. Round to the nearest cent.

Set up equation:

Show work here:

Original cost of the turkey:

C. Using the formula , find another formula that represents the markup
rate. (Hint: Solve for r.)

Markup rate formula:

D. The grocery store paid $1.99 for a 24-pack of bottled water and sold the case of water
for $6.25. Find the markup rate; round to the nearest tenth of a percent.

Show work here:

Markup rate:

Reference

Aufmann, R. N., Vernon, B. C., & Lockwood, J. S. (2006). Introductory algebra: An applied approach (7th ed.). Boston: Houghton Mifflin.