Practical Problems

By Dr. Julia Arnold

Math 04 Intermediate

Algebra

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In the problems that follow, you are going tosee developed something called amathematical 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 occasionallyseeing 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?

Excel Spreadsheetx $12.50x20 $250.00

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?

Min AT&T Sprint

x 4.95 + .10x .15x

0 4.95 0

Let x represent the number of actual minutes or part thereof used. Then the AT&T plan can be represented by AT&T = $4.95 + .10x

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.

What equation would you set up to find theexact number of minutes which make the twoplans equal?

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The mathematical model is:

AT&T plan = Sprint plan4.95 + .10x = .15xOr 4.95 = .05x

99minutes = xHad you already guessed?

Min AT&T Sprint

x 4.95 + .10x .15x

150 ???????? ????

Click on Excel Spreadsheet and find out the cost for 150 minutes.

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 tripscan he make?

20 trips

What mathematical model gives the number oftrips which make the two methods equal?

The mathematical model is:Cost of the trips = Ticket book Cost

Or4x = 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 approximately20 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 Here When finished, click the back button.