**Solve linear equations word problems worksheet :**

Here we are going to see some practice questions on the topic solve linear equations word problems.

To solve the problems given below, we need to follow the steps.

- Read the given problem carefully
- Convert the given question into equation.
- Solve the equation and find the value of unknown.

If you find it difficult to convert the given statement into equation please visit the page (Translating word problems into equations)

(1) The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

(2) Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

(3) Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

(4) Three consecutive integers add up to 51. What are these integers?

(5) The sum of three consecutive multiples of 8 is 888. Find the multiples.

(6) The ages of John and David are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

(7) The ages of John and David are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

(8) The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

(9) Baichung's father is 26 years younger than Baichung's grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

(10) The organizers of an essay competition decide that a winner in the competition gets a prize of $ 100 and a participant who does not win gets a prize of $ 25. The total prize money distributed is $ 3000. Find the number of winners, if the total number of participants is 63.

**Problem 1 :**

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

**Solution :**

Let the breadth be x m.

The length will be (2x + 2) m.

Perimeter of swimming pool = 2(l + b) = 154 m

2(2x + 2 + x) = 154

2(3x + 2) = 154

Dividing both sides by 2,

3x + 2 = 77

Subtracting 2 on both sides, we get

3x + 2 - 2 = 77 - 2

3x = 75

On dividing 3 on both sides

x = 25

2x + 2 = 2 × 25 + 2 = 52

Hence, the breadth and length of the pool are 25 m and 52 m respectively.

Let us see the solution of next problem on "Solve linear equations word problems worksheet"

**Problem 2 :**

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

**Solution :**

Let one number be x.

Therefore, the other number will be x+ 15.

According to the question,

x + x + 15 = 95

2x + 15 = 95

Subtract 15 on both sides

2x = 95 - 15

2x = 80

Divide by 2 on both sides

x = 40

x + 15 = 40 + 15 = 55

Hence, the numbers are 40 and 55.

Let us see the solution of next problem on "Solve linear equations word problems worksheet"

**Problem 3 :**

Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

**Solution :**

Let the common ratio between these numbers be x. Therefore, the numbers will be 5x and 3x respectively.

Difference between these numbers = 18

5x - 3x= 18

2x= 18

Divide by 2 on both sides

x = 9

First number = 5x= 5 × 9 = 45

Second number = 3x= 3 × 9 = 27

Hence the required numbers are 27, 45.

Let us see the solution of next problem on "Solve linear equations word problems worksheet"

**Problem 4 :**

Three consecutive integers add up to 51. What are these integers?

**Solution :**

Let three consecutive integers be x, x + 1, and x+ 2.

Sum of these numbers = x + x + 1 + x + 2 = 51

3x+ 3 = 51

Subtract by 3 on both sides

3x = 51 - 3

3x = 48

Divide by 3 on both sides

x = 16

x + 1 = 17

x + 2 = 18

Hence, the consecutive integers are 16, 17, and 18.

Let us see the solution of next problem on "Solve linear equations word problems worksheet"

**Problem 5 :**

The sum of three consecutive multiples of 8 is 888. Find the multiples.

**Solution :**

Let the three consecutive multiples of 8 be 8x, 8(x + 1), 8(x + 2).

Sum of these numbers = 8x + 8(x+ 1) + 8(x+ 2) = 888

8(x + x + 1 +x + 2) = 888

8 (3x + 3) = 888

Dividing by 8 both sides

3x+ 3 = 111

Subtract 3 on both sides

3x + 3 - 3 = 111 - 3

3x= 108

Divide by 3 on both sides

x = 36

First multiple = 8x = 8 × 36 = 288

Second multiple = 8(x + 1) = 8 × (36 + 1) = 8 × 37 = 296

Third multiple = 8(x + 2) = 8 × (36 + 2) = 8 × 38 = 304

Hence, the required numbers are 288, 296, and 304.

Let us see the solution of next problem on "Solve linear equations word problems worksheet"

**Problem 7 :**

The ages of John and David are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

**Solution :**

Let common ratio between John's age and David's age be x.

Therefore, age of John and David will be 5x years and 7x years respectively.

After 4 years, the age of John and David will be (5x + 4) years and (7x + 4) years respectively.

According to the given question, after 4 years, the sum of the ages of John and David is 56 years.

(5x + 4 + 7x + 4) = 56

12x + 8 = 56

Subtract 8 on both sides 12x + 8 - 8 = 56 - 8

12x = 48

Divide 12 on both sides

x = 4

John's age = 5x years = (5 × 4) years = 20 years

David's age = 7x years = (7 × 4) years = 28 years

**Problem 8 :**

The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

**Solution :**

Let the common ratio between the number of boys and numbers of girls be x.

Number of boys = 7x

Number of girls = 5x

According to the given question,

Number of boys = Number of girls + 8

7x = 5x + 8

Subtract 5x on both sides

7x - 5x = 5x - 5x + 8

2x = 8

Divide by 2 on both sides

x = 4

Number of boys = 7x = 7 × 4 = 28

Number of girls = 5x = 5 × 4 = 20

Hence, total class strength = 28 + 20 = 48 students

Let us see the solution of next problem on "Solve linear equations word problems worksheet"

**Problem 9 :**

Baichung's father is 26 years younger than Baichung's grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

**Solution : **

Let Baichung's father's age be x years.

Hence, Baichung's age and Baichung's grandfather's age will be (x - 29) years and (x + 26) years respectively.

According to the given question, the sum of the ages of these 3 people is 135 years.

x + x - 29 + x + 26 = 135

3x - 3 = 135

Add 3 on both sides

3x - 3 + 3 = 135 + 3

3x = 138

Divide by 3 on both sides

x = 46

Baichung's father's age = x years = 46 years

Baichung's age = (x - 29) years = (46 - 29) years

= 17 years

Baichung's grandfather's age = (x + 26) years

= (46 + 26) years = 72 years

**Problem 10 :**

The organizers of an essay competition decide that a winner in the competition gets a prize of $ 100 and a participant who does not win gets a prize of $ 25. The total prize money distributed is $ 3000. Find the number of winners, if the total number of participants is 63.

Answer :

Let the number of winners be x. Therefore, the number of participants who did not win will be 63 - x.

Amount given to the winners = $ (100 × x) = $ 100x

Amount given to the participants who did not win = Rs [25(63 - x)]

= $ (1575 - 25x)

According to the given question,

100x + 1575 - 25x = 3000

Subtract 1575 on both sides

75x + 1575 - 1575 = 3000 - 1575

75x = 1425

Divide by 75 on both sides

x = 19

Hence, number of winners = 19

After having gone through the examples explained above, we hope that students would have understood "Solve linear equations word problems worksheet".

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