Applications

1. 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.
   
   

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

   2. 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.
      
      

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

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

   5. Fill in the blank from part B. 
      
      

   6. 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.

    

2. Examples
   
   

   1. 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
      
      

      1.  Read Carefully
         
         

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

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

      4. 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 ¹3 9
             -   2 3 1  4 4    
                           9 5
         
         

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

      6. 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.
         
         

   2. 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
      

      1. Read Carefully
         
         

      2. The price per square yard is $        .
         
         

      3. square yards  =  31         Total Cost  =  1,302
         
         

      4. 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
         
         

      5. The price per square yard is $ 42   .
         
         

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

3. Exercises
   
   

   1. 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?
      
      
      

   2. 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?
      
      
      
      

   3. 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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