Applications

Strategies For Solving Application Problems
Application problems, a.k.a. word problems or story problems, traditional
pose the greatest challenge to math students. We must keep in mind,
however, that other then just enjoying math as a beautiful art form,
application problems are the main reason for studying math. What makes
these problems difficult, is that there is no set formula that tells us how
to solve them, although there are certain strategies that help guide us
towards a solution. Below are some steps that we can take to aid us in
this problem solving task.

Read the problem carefully and get
a general idea of what it is about.

Determine what the problem is
asking and write down what the final solution is in a complete sentence
leaving the numeric part blank for now.

Write down the key pieces of
information that are needed to solve this problem.

Determine what type of arithmetic
is needed to solve the problem and perform this arithmetic.

Fill in the blank from part
B.

Look at your answer. Is it
reasonable? Does it answer the question? Check your
calculation by rounding and estimation or by calculating the reverse
operation.

Examples

Leaving South Lake Tahoe, you notice your odometer reads
23,154 miles. When you arrive at your destination of Sacramento
your odometer reads 23,249. How far is it from South Lake Tahoe to
Sacramento?
Solution

Read Carefully

We want to know the distance that was driven.
The
distance from South Lake Tahoe to Sacramento is
miles.

South Lake Tahoe reading =
23,154 Sacramento
reading = 23,249

Since we want to find out how many miles were added
to 23,154 to get to 23,249, this is a subtraction problem.
1
2 3 2 ^{1}3
9
 2 3 1 4 4
9 5

The distance from South Lake
Tahoe to Sacramento is 95 miles.

This answer seems reasonable, especially if you are
familiar with the area. Had we seen a number like 9,503 we
should be concerned since this would be longer than coast to coast
travel in the US. We round each to the nearest hundredth place
to get
23,200  23,100 = 100
and see that the solution is close to
the approximate solution.

A carpet store is offers you a
deal to carpet your 31 square yard living room for only $1302.
What is the price per square yard?
Solution

Read Carefully

The price per square yard is $
.

square yards =
31 Total Cost
= 1,302

Since the number of square
yards times the cost per square yard produces the total cost, this
is a division problem:
42
31
1302

124
62
 62
0

The price per square yard is $
42 .

The cost seems reasonable. We
check by multiplying
42
+ 31
42
1260
1302

Exercises

You need to balance your checkbook for the week.
This week you make deposits for $243, $549, and $984. You wrote
out checks for $324, and $875. What is that balance of your
checkbook?

On your drive from San Francisco to South Lake Tahoe you
filled your tank in San Francisco and write down your odometer reading
of 45,689. When you arrived in South Lake Tahoe you filled up the
tank with 6 gallons of gas and noticed that your odometer read
45,875. What was your gas mileage for the trip?

A patient has a fentanyl transdermal patch that releases
50 mcg/hour. How much fentanyl will the patient receive in a 24
hour period?
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