**Expressions and equations worksheets : **

Worksheet on expressions and equations is much useful to the students who would like to practice solving real world problems using expressions and equations.

**Write each verbal phrase as mathematical expression : **

1. The sum of 7 and 3 times of a number.

2. Three less than four times of a number.

3. One fourth of 3 times of a number.

4. One fifth of sum of 3 times a number and 9

5. 7 less than 3 times the sum of a number and 6

**Evaluating expressions : **

6. Evaluate the given expression for x = 3 and y = 5.

3x + 2y

7. Evaluate the given expression for m = 5 and n = 2.

m² + 2mn²

8. Evaluate the given expression for s = 5.

s² + 7s - 2

9. Evaluate the given expression for m = 1/3.

18m² + 3m + 7

10. Evaluate the given expression for m = 13.

m² + m - 54

**Word problems :**

**11. 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 ? **

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

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

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

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

**Question 1 :**

Write the given verbal phrase as mathematical expression

"The sum of 7 and 3 times of a number"

**Answer :**

**Question 2 :**

Write the given verbal phrase as mathematical expression

"Three less than four times of a number"

**Answer :**

**Question 3 :**

Write the given verbal phrase as mathematical expression

"One fourth of 3 times of a number"

**Answer :**

**Question 4 :**

Write the given verbal phrase as mathematical expression

"One fifth of sum of 3 times a number and 9"

**Answer :**

( 3x + 9 ) / 5

**Question 5 :**

Write the given verbal phrase as mathematical expression

"7 less than 3 times the sum of a number and 6"

**Answer :**

3(x + 6) - 7

**Question 6 :**

Evaluate the given expression for x = 3 and y = 5.

3x + 2y

**Answer :**

Plug x = 3 and y = 5 in the given expression

3(3) + 2(5) = 9 + 10 = 19

Hence, the answer is 19

**Question 7 :**

Evaluate the given expression for m = 5 and n = 2.

m² + 2mn²

**Answer :**

Plug m = 5 and n = 2 in the given expression

5² + 2(5)(2)² = 25 + 40 = 65

Hence, the answer is 65

**Question 8 :**

Evaluate the given expression for s = 5.

s² + 7s - 2

**Answer :**

Plug s = 5 in the given expression

5² + 7(5) - 2 = 25 + 35 - 2 = 58

Hence, the answer is 58

**Question 9 :**

Evaluate the given expression for m = 1/3.

18m² + 3m + 7

**Answer :**

Plug m = 1/3 in the given expression

18(1/3)² + 3(1/3) + 7 = 2 + 1 + 7 = 10

Hence, the answer is 10.

**Question 10 :**

Evaluate the given expression for m = 13.

m² + m - 54

**Answer :**

Plug m = 13 in the given expression

13² + 13 -54 = 169 + 13 - 54 = 128

Hence, the answer is 128

**Question 11 :**

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 ?

**Answer :**

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.

**Question 12 :**

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.

**Question 13 :**

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.

**Question 14 :**

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.

**Question 15 :**

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.

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