LESSON NOTES ON WORD PROBLEMS LEADING TO LINEAR EQUATIONS

                                    

                                             

SUBJECT: Algebra

TOPIC: Linear Equations

LESSON: Solutions of word problems leading to linear equations in one unknown

PREVIOUS KNOWLEDGE: Students can solve linear equations

TEACHING AIDS: A chart with statements already translated to linear equations

LESSON OBJECTIVES: By the end of the lesson, students will be able to translate and solve word problems leading to linear equations in one unknown

TEACHING METHODS:  Demonstration, Question and answer, Group discussion, and Assignment.

DURATION:  45 minutes

GRADE LEVEL: 7 ( Form 2)

INTRODUCTION: 

When you add 3 to a number, your answer is 7. What is the number?  We can translate this statement into a linear equation and  solve as below.

                                 Solution

Let the number be x

Adding 3 gives; x+3

Answer is 7; x+3=7(subtract 3 from both sides)

                      x+3-3=7-3

                     x+0=4

                         x=4

PRESENTATION:

We can use linear equations to solve word problems . To solve any word problem using a linear equation, translate the word problem into a linear equation . You can use any unknown of your choice. To double a number means to multiply it by 2 and to treble a number means to multiply it by 3

Example 1: Jane thinks of a number. She adds 5 to it. Her answer is 12. Find the number

                                          Solution

Let the number be x

She adds 5; x+5

Her answer is 12; x+5=12 (solve for x)

                               x+5-5=12-5

                               x+0=7

                              x=7 answer.

Example 2: I think of a number. I subtract 6 from it and my result is 9. Find the number.

                                       Solution

Let the number y

I subtract 6; y-6

The result is 9; y-6=9 (solve for y)

                          y-6+6=9+6

                          y-0=15

                           y=15 answer.

Example3: Jemia thinks of a number. He multiplies it by 3 and adds 6.the result is 18. Calculate the number.

                                                           Solution

Let the number x.

He multiplies it by 3; 3x.

Adds  6; 3x+6 .

Result is 18; 3x+6=18 (solve for x)

                       3x+6-6=18-6

                       3x+0=12

                          3x=12 (divide both sides by 3)

                         3x=12

                          3    3

                          x=4 answer

Example 4: Eyong thinks of number. He divides it by 4 and subtracts 1.His answer is 9. Find the number.

                                       Solution

Let the number be k.

Divide  by 4 ; k

                        4

Subtracts 1; k   -1

                      4

Result is 9;  k  -1=9 ( solve for K)

                     4

K -1+1=9+1

4

K –0=10

4

K×4=10×4

4

k×1=40

k=40 answer

Example 5: A boy has $500 more than another. Both have $1100 within them. How much does each have?

                                                Solution

Let b₁ represent first boy and b₂ represent second boy.

Let b₁ have $x and b₂ have $(x+500).

Both have $1100; $x+$(x+500)=$1100

Linear Equation: x+x+500=1100

                              2x+500=1100

                           2x+500-500=1100-500

                            2x+0=600

                              2x=600

                              2x =600

                               2      2

                                x=300

b₁=$300, b₂=$800

EVALUATION:

Solve the following :

i)                    Peter thinks of a number. He adds 6 to it.  The result is 14,find the number.

ii)                   Evelyn added  4 to a certain number. He multiplied by 5 and then added 8. If the final result is 48, find the number.

CONCLUSION:

         Assignment

iii)                 I think of a number and double it.I divide the result by 3. My answer is 8. Find the original number.

iv)                 A father is 20 years older than his son. Find the son’s age when he is 1 of his father’s age                                                                                             5
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