LINEAR EQUATIONS (LECTURE 6)

LINEAR EQUATIONS EX 2.4(I)
DEAR STUDENTS
WELCOME TO THE CLASS!!

LET'S GO THROUGH THE RULES OF THE BLOG

Guidelines for the class:

1. Note down  the work in your register on a regular basis.

2. Please feel free to ask, if you have any doubt by dropping a message in the comment box.

3. Make a column on the right hand side, if you need to do any rough work

4..Write today's date.

5.Write the chapter number and name.

6.Text in Blue has to be noted down.

let's recall the  learning outcomes we covered  yesterday:

Solving linear equations having variables on both the sides.

Write down Today's Learning Outcomes

I will be able to:

. translate the word problems in the form of linear equations

.solve the linear equation to find the unknown.

Today we will start with Ex 2.4 which comprises of word problems.

LET'S REVISE  5 Steps to Solve Word Problems (Note down)

1. Read through the problem carefully.
2. Ask yourself a question" What am I looking for"?.
3. Let the thing " you are looking for" be x.(or any other variable)
4. Make a linear equation using x and the information given.
5. Solve the linear Equation.

We will first start with AGE RELATED WORD PROBLEMS

NOTE DOWN SOME KEY POINTS :

1.If the present age is x then five times present age is '5x'

2.If the present age is x  then age five years hence/after/from now  is x +5

3.If the present age is x  then age 5 years  before/ago   is x -5.

4. If age of one boy is x years then age of his sister :

a) who is 4 years older to him = x+4

b)who is 3 years younger to him = x - 3

Click on the link to learn more

Now look at the  eg of your book

 Ques  Arjun is twice as old as Shriya . Five years ago his age was three times Shriya’s age. Find their present ages.

Let us take Shriya’s present age to be x years.

why did we take shriya's age as x and not arjun's age??

Then Arjun’s present age would be 2x years.

 Shriya’s  age five years ago was (x – 5) years (remember the key word ago which means '-').

 Arjun’s age five years ago was (2x – 5) years. 

It is given that Arjun’s age five years ago was three times Shriya’s age.

 Thus, 2x – 5 = 3(x – 5) ( key word times means multiply)

or 2x – 5 = 3x – 15 (solve the bracket)

15 – 5 = 3x – 2x or 

10 = x

 So, Shriya’s present age = x = 10 years. 

Therefore, Arjun’s present age = 2x = 2 × 10 = 20 years.

LET'S START WITH AGE RELATED QUESTIONS OF EX 2.4

10. Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

It is quite similar to the example done above

so, whose age we will assume as 'x'?

son's age. 

let son's age  be 'x' years

so, as per question

Aman's age will be 3x  (remember the key word 'times')

ten years ago

3x -10   =  5x -50

50 -10 =5x -3x

40 = 2x

  x = 20 years

Hence, Aman’s son’s age = 20 years

And Aman’s age = 3 X20 = 60 years


5. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages? 

Let Shobo’s present age be  years.

And Shobo’s mother’s present age =  years

According to the question,  

 

 

 

 years.

Hence, Shobo’s present age = 5 years

And Shobo’s mother’s present age =  = 30 years.

I HOPE YOU HAVE FOLLOWED HOW TO DO AGE PROBLEMS.


LET'S START WITH " FIND THE NUMBER" PROBLEMS

FIRST WE WILL REVISE THE KEY WORDS(note down)

1.   5  MORE THAN X  OR 5 ADDED TO X                                X +5

2. 5 LESS THAN X  OR 5 SUBTRACTED FROM X                   X -5

3. X LESS THAN 5                                                                           5 -X

4. RATIO/QUOTIENT OF 5 AND X                                          5/X

5. DOUBLE/TWICE  THE NUMBER X                                  2X

LET.S START WITH Q1 OF EX 2.4

 Q1 Amina thinks of a number and subtracts 5 /2  from it. She multiplies the result by 8. The  result now obtained is 3 times the same number she thought of. What is the number?
 Here what are we looking for?
Ans. we are looking for a number.

so, Let the number be x

1. Amina subtracts 5/2 from the number

we get,  x -5/2

2. She multiplies the result by 8

we get, 8(x - 5/2) ( don't forget the bracket)

3. The  result now obtained is 3 times the same number she thought of

we get, 8(x - 5/2) = 3x  (3 times the number is 3x)

simplifying,  8x - 20 = 3x  
=>  8x - 3x = 20 (shift 3x to LHS and 20 to RHS)

=> 5x =20
=> x =20/5= 4

so, the number is 4

EX 2.4 Q2 AND 9

WE WILL FINISH OUR CLASS HERE!1
SEE U TOMORROW!!