Practical Problems n By n Dr. Julia Arnold n Math 04 n Intermediate Algebra Click on icon for sound.

In the problems that follow, you are going to see developed something called a mathematical model. When trying to interpret practical application problems, we try to find a mathematical model for the problem. Many times this simply requires some common sense, and occasionally seeing some other examples. So, let’s begin…………………………………

Example 1: Should I keep going to the Laundry Mat? Suppose it costs you $12.50 a week to wash and dry your clothes at the local laundromat. You just found a washer and dryer selling for $940. Disregarding any other factors, if you buy the washer and dryer, in how many weeks will you start saving money?

Always identify variables: Let x = the number of weeks before you will recognize any savings. Using an Excel Spreadsheet, we can do some guessing and have some idea about the number of weeks. Example: To access the spreadsheet, click on the word Example. When finished with the spreadsheet, click the back button.

The mathematical model for this problem is: (Cost of doing laundry per week) times (number of weeks) = (cost of washer and dryer) Or 12.50x = 940 Thus x = 75.2 weeks

Example 2: Which long distance carrier to pick? You are a business person who usually makes at least 150 minutes of long distance calls per month. You want to choose the most economic long distance plan. You find AT&T offers a plan that requires you to pay a monthly fee of $4.95 plus 10 cents per minute, or part thereof. Sprint has a plan that does not have a monthly fee, but the customer pays 15 cents per minute, or part thereof. Which plan should you pick?

Let x represent the number of actual minutes or part thereof used. Then the AT&T plan can be represented by AT&T = $ x How can we represent the Sprint plan? Sprint =.15x Can you find the number of minutes or part thereof which would make the two equal? Click on Excel Spreadsheet and try to guess the exact answer.Excel Spreadsheet

What equation would you set up to find the exact number of minutes which make the two plans equal? Need Help? Click Here

The mathematical model is: AT&T plan = Sprint plan x =.15x Or 4.95 =.05x 99minutes = x Had you already guessed? Click on Excel Spreadsheet and find out the cost for 150 minutes.Excel Spreadsheet

Which plan gives the best value for our business person? Check your answer: AT& T would be the best choice for our business person because 150 minutes would only cost $19.95 per month while the Sprint plan would end up costing $22.50 per month.

Example 3: The cost of getting to work? Scott Jones lives in New Jersey and works in New York. He commutes over the George Washington Bridge to go to work 5 days a week. The GW Bridge costs $4 for a car going from New Jersey to New York, but there is no cost going from New York to New Jersey. Individuals can purchase a number of different non-refundable discount ticket books. One, called the All Bridges Book, costs $60 and contains 20 tickets. How many trips to New York would Scott need to make so that buying the ticket book is worthwhile? See if you can solve the problem.

What should x equal? Let x = number of trips from NJ to NY. What is the cost of each trip from NJ to NY? $4.00 What is the cost of the ticket book? $60 If Scott buys the ticket book, how many trips can he make? 20 trips What mathematical model gives the number of trips which make the two methods equal?

The mathematical model is: Cost of the trips = Ticket book Cost Or 4x = 60 x = 15 trips Should Scott (a) pay the $4 each time or (b) buy the ticket book Assuming a 4 week month, how many times on average will Scott travel to NY per month? Scott will travel approximately 20 times per month. B is correct he should buy the book otherwise he would pay $80

You are ready to experience some problems for yourself. You will see some problems from Math 03 (or elementary algebra), some problems similar to the examples, and some in which you can apply the “solving systems” section you just finished. The Fun Begins by Clicking HereThe Fun Begins by Clicking Here When finished, click the back button.