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## Forming Linear Equations in One Variable Worksheet

**Example 1**. One of the numbers is two times the other. The sum of these two numbers is 45. Form the equation to find the numbers using a linear equation in one variable?

**Solution:**

Let the number be x

The Other Number is 2 times the given number i.e. 2x

From the given condition, the sum of these two numbers is 40

We can write the equation x+2x=45

3x=45

x=45/3

x=15

The other number is 2x i.e. 2(15)=30

**Example 2.
**The perimeter of a rectangular swimming pool is 140 meters. Its length is 4 m more than twice its breadth. What are the length and breadth of the pool?

**Solution:**

Let the breadth of the rectangular swimming pool be x

Since length is 4m more than twice its breadth we can have length = 2x+4

Perimeter of a Rectangular Swimming Pool = 2(l+b)

140 =2(2x+4+x)

140=2(3x+4)

140=6x+8

140-8=6x

132=6x

x=132/6

x=22

Length l =2x+4

=2(22)+4

=44+4

=48

Thus, the breadth and length of the swimming pool are 22m and 48m respectively.

**Example 3.
**The sum of three consecutive odd numbers is 45. Find the numbers?

**Solution:**

Let the three odd consecutive numbers be x, x+1, x+2

As per the given condition sum of three consecutive odd numbers is 45

x+x+1+x+2=45

3x+3=45

3x=45-3

3x=42

x=42/3

x=14

x+1=14+1=15

x+2=14+2=16

Therefore, the three consecutive numbers are 14, 15, 16

**Example 4.
**A sum of Rs. 4500 is to be given in the form of 90 prizes. If the prize is of either Rs. 100 or Rs. 25, find the number of prizes of each type?

**Solution:**

Let us assume the type of 100Rs prizes be x

Since the total number of prizes is 90 the number of 25 Rs. prize is 90-x

As per the given data in the question

100*x+(90-x)=4500

100x+90-x=4500

99x+90=4500

99x=4500-90

99x=4410

x=4410/99

__~__44

Therefore 25Rs. Prizes are 90-44 = 46

**Example 5.
**A dealer sold a television set for Rs. 12,000 and earned a profit of 15%. Find the cost price of the television set?

**Solution:**

Selling Price of the Television = Rs. 12,000

Let us assume the cost price = x

Profit earned = 15%

Cost Price of the television set CP = (100 / ( 100 + percentage profit))*SP

=(100/(100+15)*12000

=(100/115)*12000

=Rs. 10434

Therefore, the dealer bought the television set for a cost price of Rs. 10434

**Example 6.
**Twenty years from now Rahul’s age will be 5 times his current age. What is his current age?

**Solution:**

Let us consider the current age of Rahul as x

Twenty Years from now his age would be x+20

As per the given condition in the question we have x+20=5x

20=5x-x

20=4x

20/4 =x

x=5

Therefore current age of Rahul is 5 Years.

**Example 7.
**Solve 2y -10 = 4

**Solution:**

Given Expression is 2y-10=4

Transfering constants to one side and variables to the other side we have 2y =4+10

2y=14

y=7

**Example 8.
**Rajesh is a cashier in a State bank. he has notes of denominations of Rs. 100, 50, and 20 respectively. The ratio of the number of these notes is 4:3:2 respectively. The total cash with Rajesh is 4,72,000. How many notes of each denomination does he have?

**Solution:**

Let us assume the numbers of notes be 4x, 3x, and 2x respectively based on the ratio of notes

100*4x+50*3x+20*2x =4,72,000

400x+150x+40x=4,72,000

590x=4,72,000

x=4,72,000/590

=800

No. of 100 Rs Notes Rajesh has = 4x

=4*800

=3200

No. of 50 Rs Notes Rajesh has = 3x

=3*800

=2400

No. of 20 Rs Notes Rajesh has = 2x

=2*800

=1600

**Example 9.
**Solve for 8x + 40 = 4x +100?

**Solution:**

Given Expression is 8x + 40 = 4x +100

Transferring the constant terms to one side and variables terms to another side we have

8x-4x=100-40

6x=60

x=10

**Example 10.
**Amar thinks of a number and subtracts 3/2 from it. She multiplies the result by 7. The final result is 4 times her original number. Find the number?

**Solution:**

Let the number be x

From the given statement we can infer 7(x-3/2)=4x

7x-21/2=4x

(14x-21)=2*4x

14x-8x=21

6x=21

x=21/6

Therefore, the number is 21/6