# Solving linear equations and word problems

MTH212

Unit 1 - Individual Project A

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. The cell phone service for the CEO of a small company is $39.99 a month plus $0.10

per minute for long distance. In a month when the company's phone bill was $75.19,

how many minutes of long distance did the CEO use? Set up an equation and solve.

Show all work to receive full credit.

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.

Two runners, Jay and Ben, start at the same time from opposite ends of an 8-mile jogging trail and begin running toward each other. Jay is running at the rate of 5 mph, and Ben is running at a rate of 7 mph. How long, in minutes, after they start will Jay and Ben meet?

A. Who will have traveled the longer distance?

Answer:

B. When they meet, what is the combined distance Jay and Ben will have traveled?

Answer:

C. What equation represents this situation?

Answer:

D. Solve the equation; show work your here:

Answer:

E. How long, in minutes, did it take for Jay and Ben to meet?

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; it must be detailed to receive full credit:

Answer:

6. A clothing store may reduce the regular price of a product because the clothes are damaged, odd sizes, or discontinued items. The discount, or markdown, is the amount by which the store reduces the regular price of a product. The percent discounted is called the discount rate and is usually expressed as a percent of the original selling price. Taking the regular price and subtracting the discount calculates the sale price. The formula can be used to help find the sale price. The sale price, S, is equal to the regular price, R, minus the discount rate, r, multiplied by the regular price, R (Aufmann, Vernon, & Lockwood, 2006).

Using the aforementioned information, solve the following problems.

A. A pair of shoes that are currently selling for a price of $89.99 are going to be marked down 20% for the spring sale. Use the sale price formula to find the new

price of the shoes. Round to the nearest cent.

Set up equation:

Show work here:

Sale price of shoes:

B. A suit coat that is marked down 35% has a sale price of $292.50. Use the sale price

formula to find the regular price of the suit coat. Round to the nearest cent.

Set up equation:

Show work here:

Regular price of the suit coat:

C. Using the formula , find another formula that represents the discount

rate. (Hint: Solve for r.)

Discount rate formula:

D. A prom dress with a regular price of $395 is on sale for $280. Find the discount rate;

round to the nearest tenth of a percent.

Show work here:

Discount rate:

Reference

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

© BrainMass Inc. brainmass.com April 3, 2020, 5:26 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/solving-linear-equations-and-word-problems-160488

#### Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.

===============================================================================

MTH212

Unit 1 - Individual Project A

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

Show work here:

2x - 8 = 2[x - 3x + 3 +2}

2x - 8 = 2[-2x +5]

2x - 8 = - 4x + 10

6x = 18

x = 3

Final Answer: x = 3

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

Show work here:

Multiply by the common factor: common factor is 18

6(x-2) - 3(x+5) = 2(5x-2)

6x - 12 - 3x - 15 = 10x - 4

6x - 3x -10x = -4 +15 +12

-7x = 23

Final Answer:

3. The cell phone service for the CEO of a small company is $39.99 a month plus $0.10

per minute for long distance. In a month when the company's phone bill was $75.19,

how many minutes of long distance did the CEO use? Set up an equation and solve.

Show all work to receive full credit.

Equation:

Monthly bill = 39.99 + 0.10 x

where x is the number of minutes of long distance call.

Show work here:

Monthly bill = 39.99 + 0.10 x

75.19 = 39.99 + 0.10 x

0.10 x = 35.20

x = 352 min.

Final Answer: ...

#### Solution Summary

This 6-page word document contains answers to six lengthy questions related to solving linear equations. Some questions are word problems with several sub categories. I have provided clear solutions to all the problems.