AL3 Algebra : Word Problems

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COMMON TERMS in WORD PROBLEM / PROBLEM SUM

(1) Read the sentence carefully and spot the word patterns.

(2) Note (a) the Object/What/Who's and (b) the number/fractions in the sentence.

(3) Form equation to link objectss and numbers

Thus, the 3-steps:

  Step 1:  What the Who/What?Underline/Circleand write Symbols/Number

  Step 2:  Who/What’s numbers(N)? Draw and link.

   Step 3: Solve by Equation

Example1

Alvin is Y years old. His mother is 4 times as old as Alvin. His father is 5 years older than his mother. If Y = 8, how old is his father?

Method

Step 1:  What the Who/What?Underline/Circle and write Symbols/Number

            W                N

            Alvin            Y

            Mother

            Father

Step 2:  Who/What’s numbers(N)? Draw and link.

            W                N
            Alvin            Y

            Mother        4Y

            Father            4Y + 5

Step3: Solve: Link to form an equation

                        Y = 8

            His father is (4 x 8) + 4 = 36 years old.

Example2

The perimeter of a rectangle is (2b + 8) cm. If the length is b cm, what is the breadth?

Method

Step 1:  What the Who/What?Underline/Circle and write Symbols/Number

            W                N

            Perimeter   (2b + 8)  

            Length          

            Breadth

Step 2:  Who/What’s numbers(N)? Draw and link.

            Actor               Symbol/numbers

            Perimeter      2b + 8

            Length           b

            Breadth          U (Let U be the breadth)

Step3: Solve: Link to form an equation

            (Link by Formula: Perimeter = 2length + 2 Breadth)

            2b + 8 = 2b + 2U

            2U + 2b = 2b + 8

            2U + 2b – 2b = 2b -2b + 8

            2U = 8

            2U / 2 = 8 /4

            U = 4cm

Example3

A pen costs $p and a file costs $2 more than a pen. After paying for 1 file and 2 pens, John has left $0.50 left. If the pen costs $2.50, how much money does John have at first?

Method

Step1: 
            W                          N

            J’s Pen                  p                    

            J’s File                  p + 2

Step 2

            W                          N

            J’s Pen                  p                     

            J’s File                  p+2

            John bought 1 file and 2pens. 1 pen = $2.50
Step3: 

            The cost p + 2 + 2p = 3 x 2.5 + 2

                                                = 7.5 + 2

                                                = $9.50

            He is left with $0.50

            He has $9.50 + $0.50 = $10 at first.

Example4

John had 12 more pies than Clive at first. After John ate 4 pies, he had twice as many pies as Clive in the end. How many pies did Clive have?

Method

Step1: 

     Let U be Clive’s pie.

                        John     U + 12

                        Clive     U

Step 2:  

                        John   U + 12 – 4 (12 more pies than Clive, then ate 4)

                        Clive   U 

Step3: 

            Form an equation by ‘equalizing’ the pies they have.

                        John has twice as many pies as Clive

                        -> 2 times of Clive’s pie = John’s pie

                            2U = U + 12 – 4

                            2U – U = U + 12 – 4 – U

                              U = 12 – 4

                              U = 8

Clive has 8 pies.