# Practical

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```					      Practical Problems
  By
 Dr. Julia Arnold
 Math 04
 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.

To access the
Example:
spreadsheet, click on
the word Example.
When finished with
Excel Spreadsheet
the spreadsheet,         x      \$12.50x
click the back button.
20      \$250.00
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 = \$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
Min       AT&T          Sprint    try to guess the
exact answer.
x         4.95 + .10x   .15x
0          4.95       0
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
4.95 + .10x = .15x
Or 4.95 = .05x
99minutes = x
Had you already guessed?
Click on Excel
Min      AT&T          Sprint    Spreadsheet and
find out the cost
x        4.95 + .10x   .15x      for 150 minutes.

150 ????????       ????
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
Assuming a 4 week month, how many times on
average will Scott travel to NY per month?

Should Scott (a) pay the \$4 each time or
(b) buy the ticket book
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 Here
When finished, click the back button.

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