# Writing and solving equation from word problem worksheet

In the case of a word problem, first, we form the equation from the given statement and then solve it.

### Procedure to solve the word problem

Step: 1 Read the given question carefully and try to understand what is given and what we have to find .

Step: 2 Denote unknown quantity of equation by x, y , z,,,, etc .

Step :3 Try to understand the relationship between the given quantities and the unknown quantities.

Step;4 Form the equation using the given information .

Step; 5 Solve the obtained equation (Find the value of unknown quantity in the equation )

Step:6 To check the correctness of the equation, substitute the solution of the unknown quantity in LHS and RHS. It must be equal

Let’s see some problems to understand this concept clearly

Q.1 Length of a rectangle is 5 m less than twice its breadth. If the perimeter of the rectangle is 62 m, find its length and breadth

Solution:

Given information :

We have a rectangle whose length is 5 m less than twice its breadth and its perimeter is 62 m.

Let the breadth of the rectangle be x  m

Then , its length be (2 × breadth – 5 ) = ( 2x – 5)

We know , perimeter of the rectangle = 2{Length(l) + breadth(b)}

Perimeter of the rectangle = 2{2x – 5 + x}

Perimeter of the rectangle =2{x – 5}

Since , perimeter of the rectangle is 62 m

2{x – 5}= 62

2x – 10 = 62

2x = 62 + 10

2x = 72

x= 36

So, breadth of the rectangle is 36 m

and , Length of the rectangle = ( 2x – 5) = 2×36 – 5 = 72 – 5 = 67 m

Q.2 The sum of two consecutive numbers is 175 .Find the numbers

Solution:

Given information :

The sum of two consecutive numbers is 175 .

To learn about consecutive numbers ,check this

Let one of the number be x .Then the second number will be x + 1

∴ x + x + 1 = 175

2x + 1 =175

2x =175 – 1

2x = 174

x = 87

So, two required consecutive numbers are 87 and 88.

Q.3 Age of Muskan’s father is 4 years more than 5 times Muskan’s age. What is the present age of the Muskan, if her father is 34 years old?

Solution:

Given

(i) Muskan’s father present age is 34 years

(ii) Age of Muskan’s father is 4 years more than 5 times Muskan’s age

Let the Present age of the Muskan be x year.

Muskan’s father age = 5 (Muskan age ) + 4

Muskan ‘s father age = 5 x + 4

∴ 5x + 4 = 34

5x = 34 – 4

5x = 30

x = 6

Hence , Muskan’s age 6 years old

Q. 4 Sum of 3 consecutive integers is 24 .Find the integers

Solution:

Let the three consecutive integers are x , x + 1 and x + 2 .

Since , sum of 3 consecutive integers is 24

∴ x + x + 1 + x +2 = 24

3x + 3 = 24

3x = 21

x =7

Hence , Three consecutive numbers are 7, 8 and 9 .

Q.5 A wallet contains the same number of 2 – rupee coins and 5 – rupee coins.The total value of these coins is 70 Rs .How many of each type of coin does the wallet contain ?

Solution:

Given :

Total value of coins in the wallet = 70 Rs

and , wallet contains the same number of 2 – rupee and 5 – rupee coins

Let the number of 2 -rupee and 5 – rupee coins be x

Value of one 2 -rupee coin = 2 Rs

Value of one 5 – rupee coins = 5 Rs

∴ Value of x 2 -rupee coin = 2x Rs

Value of x 5 – rupee coins = 5x Rs

Total value of 2 -rupee and 5 – rupee coins = (2x + 5x) Rs

2x + 5x =70

⇒ 7x = 70

⇒ x = 10

Thus , number of 2-rupee coins = 10 and number of 5 – rupee coins = 10

Check these stuff as well

Don’t forget to comment your feedback in the comment section