Problem solving is a method through which a problem is solved using systemmatic steps.

1. The first step in solving a problem is to first understand or comprehend the problem being asked. That is, what is the exact question you need to answer?

2. Next, it is necessary to figure out what information is already given, and what other information you may need to know in order to answer the question.

3. Disregard any information that would not be needed to solve the question.

4. You can re-write the question in your own words with only the necessary information.

5. You can also draw pictures in-order to get a clear idea of what the problem is.

6. If it is a big problem, it is necessary to break down the problem into smaller parts.

7. Re-check your work.

Sherry scored 82 on her first test, 82 on her second test, 76 on her third test and 94 on her fourth test. What score must she receive on her fifth test to maintain an average of 86?

1. What is the problem to be solved?

• The problem is what must Sherry's fifth test score be to get an average of 86?

2. What do we know and what do we not know?

• We know the scores for the first 4 tests.

They are 82, 82, 76, and 92.

• We know the sum of the first four tests.

82 + 82 + 76 + 92 = 332

• We know how to calculate the average or mean.

Average or Mean = sum of the numbers / number of numbers

• We know the number of tests she has.

Number of tests = 5

• We know the average.

Average or Mean = 86

• We do not know the fifth score.
  
  
  
• We do not know the total.

In this example only two of the seven steps were necessary in solving this problem.




- Let us say that the fifth score is T

- The sum of the five numbers is

82 + 82 + 76 + 92 + T = 332 + T

- Average = sum of the numbers / number of numbers

86 = 332 + T / 5

or

86 / 1 = 332 + T / 5

- Cross Multiply

(332 + T) x 1 = 86 x 5

332 + T = 430

T = 430 -332

T = 98

The fifth test score is 98

If a piece is string which is 40 centimeters long, is cut into 3 pieces. To cut string into three pieces will require two men. The two men will take at least 1 minute to cut the string. The longest piece is three times the length of the middle sized piece and the shortest piece is 23 centimeters shorter that the longest piece. Find the lengths of each of the three pieces of string?

1. What is the problem?

The problem is to find the lengths of the three pieces of string

2. What do we know and what do we not know?

• We know the length of the entire string

Length of string = 40 centimeters

• We know the number of pieces the string is cut into

Number of pieces = 3 pieces

• We do not know the exact length of each piece of string

3. What information is not necessary?

"To cut string into three pieces will require two men. The two men will take at least 1 minute to cut the string."

4. Re-write question.

String is 40 centimeters long. String is cut in 3 pieces. The shortest piece is 23 centimeters shorter thant longest piece. Longest piece is 3 times the middle sized piece.

5. Draw a picture

________|__________________|____________________________

<----------------------------40cm------------------------------>

The longest piece, L3, is 3 times the length of the middle sized piece

L3 = 3x

The length of the middle sized piece, L2, is x

L2 = x

The shortest piece, L1, is 23 centimeters shorter than longest

L1 = 3x - 23

Total = L1 + L2 + L3

L1 + L2 + L3 = 40

3x - 23 + x + 3x = 40

Length of x will be

7x - 23 = 40

7x = 40 +23

7x = 63

x = 9 cm

The length of the shortest piece :

L1 = 3x - 23

L1 = 3(9) - 23

L1 = 27 - 23 = 4 cm

The length of the middle piece :

L2 = x

L2 = 9 cm

The length of the longest piece :

L3 = 3x

L3 = 3(9)

L3 = 27 cm