Problem Solving

• George Polya wrote a book How to Solve It
  • It addresses general problems solving.
  • He gives a 4 step method.
    1. Understand the problem
    2. Devise a plan
    3. Carry out the plan to solve the problem.
    4. Check the answer.
  • On page 27, Blitzer gives a list of ideas, especally for step 2.
  • I have found steps 1 and two to sort of go hand in hand
    • To solve a problem you must understand it.
    • In the process of understanding, you often devise a plan on how you will solve this problem.
• Some Examples
  1. Problem 2, page 34
  2. Problem 6
  3. Problem 12

        We need to find gallons of gas burned.
        We know miles and MPG
     
        Plan
           1. Find miles traveled.
           2. Multiply this by GPM
     
        Miles:  37,364-25,124= 12,240 miles
     
                        1 gallon
        12,340 miles x  ---------  = 510 gallons
     		   24 miles
     

  4. 14

     Problem
         We know shots and point values for each team.
         We want to know who won (had the higher point value)
     Plan
         Find scores
         Compare them.
     Action
         34x2 + 13 = 81 points
         38x2 + 8 = 81 points
     
         The second team won.
     	

  5. 20

     Problem:
          We want to find out how many shares of stocks she can buy
          We know salary and expenses.
     Plan:
         Find total income
         Find total expenses
         Find difference.
         Compute how many stocks can be purchased.
     Action
        Total Income = 2750x12 = 33,000
        Rent                      4,800
        Food                      8,200
        Clothing                  4,250
        Other                     3,000
     
        Total Remaining         12,750
        
                             1 share 
        Shares:    $12,750 x ------- = 34 shares
                               $375
     	

  6. 22

     Find profit on juice sold
     Find loss on juice not sold
     
     	

  7. If time, 24, 26,

Homework