# Equations and word problems

Solve the following problems showing all your work every step of the way:

1. The following equation describes a person's optimum heart rate in beats per minute that should be achieved during exercise so that the exercise is most beneficial.

Heart rate = 0.6(220-a)

where a represents the age of the person in years.

Determine the optimum heart rate for a 35-year-old runner.

2. Research: One of the most famous formulas in the world was formulated by Albert Einstein. The formulas is E = mc2 . Use the library or the internet to research this formula and explain each variable and what the formula represents.

3. Write three different equations that have the solution of 5.

4. Set up the following problem as an equation and then solve. Tom's Rent-A-Heap Agency charges $150 per week plus $0.15 per mile to rent a small vehicle. How many miles can you travel for $550? Show your work.

In your own words, please post a response to the Discussion Board and comment on other postings. You will be graded on the quality of your postings.

(If you have any tips for me to get an understanding of math, I would be so grateful)!

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#### Solution Preview

The solution is below.

1. We are told the runner is 35 years old. So to get his optimum heart rate, we just need to substitute a=35 into the formula:

Optimum heart rate=0.6(220-35)=0.6(185)=111

2. This is the mass-energy equivalence formula. It describes the energy contained by a body by virtue of its mass.

E is the energy, measured in Joules.

m is the relativistic mass, measured in kilograms.

c is the speed ...

#### Solution Summary

This provides examples of using equations to solve word problems.

Six lengthy questions on solving linear equations including 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.

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