LINEAR EQUATIONS EX 2.2 CONT. (LECTURE 4)

LINEAR EQUATIONS EX 2.2(ii)
Good morning boys............

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 red has to be noted down as its your class work.

7. Text in green has to be read thoroughly and understood.

In the previous class ,we have solved some of the word problems....................

Today we are going to continue the same process as comprehending the word problems and converting the same into mathematical equation to find the solution.

Let us go through the procedure:

● Read the linear problem carefully and note what is given in the question and what is required to find out. 

● Denote the unknown by any variable as x, y, ……. (any variable) 

● Translate the problem to the language of mathematics or mathematical statements. 

● Form the linear equation in one variable using the conditions given in the problems. 

● Solve the equation for the unknown. 

● Verify to be sure whether the answer satisfies the conditions of the problem

Do these examples in your register

Example 1:  Bansi has 3 times as many two-rupee coins as he has five-rupee coins. If
he has in all a sum of Rs 77, how many coins of each denomination does he have?

Solution: Let the number of five-rupee coins that Bansi has be x. Then the number of
two-rupee coins he has is 3 times x or 3x.
The amount Bansi has:
(i) from 5 rupee coins, Rs 5 × x = Rs 5x
(ii) from 2 rupee coins, Rs 2 × 3x = Rs 6x
Hence the total money he has = Rs 11x
But this is given to be Rs 77; therefore,
11x = 77
or x =
77
11 = 7
Thus, number of five-rupee coins = x = 7
and number of two-rupee coins = 3x = 21 (solution)
(You can check that the total money with Bansi is Rs 77.)

Example 2: Deveshi has a total of Rs 590 as currency notes in the denominations of
Rs 50, Rs 20 and Rs 10. The ratio of the number of Rs 50 notes and Rs 20 notes is 3:5.
If she has a total of 25 notes, how many notes of each denomination she has?

Solution: Let the number of Rs 50 notes and Rs 20 notes be 3x and 5x, respectively.
But she has 25 notes in total.
Therefore, the number of Rs 10 notes = 25 – (3x + 5x) = 25 – 8x
The amount she has
from Rs 50 notes : 3x × 50 = Rs 150x
from Rs 20 notes : 5x × 20 = Rs 100x
from Rs 10 notes : (25 – 8x) × 10 = Rs (250 – 80x)
Hence the total money she has =150x + 100x + (250 – 80x) = Rs (170x + 250)
But she has Rs 590. Therefore, 170x + 250 = 590
or 170x = 590 – 250 = 340
or x =
340
170 = 2
The number of Rs 50 notes she has = 3x
= 3 × 2 = 6
The number of Rs 20 notes she has = 5x = 5 × 2 = 10
The number of Rs 10 notes she has = 25 – 8x

= 25 – (8 × 2) = 25 – 16 = 9.

EXERCISE 2.2
 QUESTION 11.to 14
 (DO THESE IN YOUR REGISTER)

This is more than enough for a day...
Boys you practice the same questions again in your rough copy by converting the statement into equations by yourself.
Please refer SDG 11 and write in your register.

See  you in the next class with rest of this exercise 2.2 and bit more....

Thank you Boys.Have  a great day.