# Linear Algebra Problems Question Set

See attached file for full problem description.

1. Solve -3[5+2(-7+x)+x]=-3x-(x+3).

2. Solve -(4x+4)/5 = (5x -1)/2 - x/3.

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.

4. The equation d=rt 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?

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

C. What equation represents this situation?

D. Solve the equation; show your work here:

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

5. Solve the following two equations separately: 3x +2(x+4)=-x+8+6x and 3x + 4 = -3(-7-x)

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

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.

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.

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

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.

Reference

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

#### Solution Summary

The solution is comprised of detailed, step by step solutions to all the linear algebra problems provided.