Practical Problems

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Practical Problems

• By
• Dr. Julia Arnold
• Math 04
• Intermediate Algebra

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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, lets begin
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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?
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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 spreadsheet, click on the word
Example. When finished with the spreadsheet,
click the back button.
Example
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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
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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 ATT 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?
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Let x represent the number of actual minutes or
part thereof used. Then the ATT plan can be
represented by ATT 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.
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What equation would you set up to find the exact
number of minutes which make the two plans equal?
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The mathematical model is
ATT plan Sprint plan 4.95 .10x .15x
Or 4.95 .05x
99minutes x
Had you already guessed?
Click on Excel Spreadsheet and find out the cost
for 150 minutes.
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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.
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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.
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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?
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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
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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.