ADDITIONAL QUESTIONS AND ANSWERS

**1) Convert the following statements into equations:**

**a) One-fourth of m is 2 more than 5.**

**Ans:** 1/4 × x = 5 + 2

x/4 = 7

**b) 2 added to 5 times q gives 17.**

**Ans:** 5q + 2 = 17

**c) Two – third of a number subtracted from 50 gives 82.**

**Ans:** 50 – 2/3 × x = 82

50 – 2x/3 = 82

**d) Seven added to seven times a number gives 107.**

**Ans:** 7x + 7 = 107

**e) 6 added to thrice a number gives 2 more than 48.**

**Ans:** 3x + 6 = 48 + 2

3x + 6 = 50

**2) Write the following equations in statement form:**

**i) 3z + 6 = 1 **

**Ans:**

6 added to 3 times z plus 6 gives 1.

**(ii) 10x = 20 **

**Ans:**

10 times x gives 20.

**(iii) m/2 + 5 = 15 **

**Ans:**

5 added to 1/2 of m gives 15.

**(iv) 3m + 3 = 98 **

**Ans:**

3 added to 3 times m gives 98.

**(v) 3s/4 = 12**

**Ans:**

Three-fourth of s gives 12.

**3)If p + 7 = 10, find the value of 9p – 50**

**Ans:** p + 7 = 10

p = 10 – 7 → p = 3

Substituting p = 3 in 9p – 50 we get,

9p – 50

9 × 3 – 50 = 27 – 50 = – 23

**4) Solve the following equations:**

**i) 4 ( q + 3 ) = 18 (ii) – 4 ( m + 3 ) (iii) 3 ( t – 4 ) = 27
**

**i) 4 ( q + 3 ) = 18**

Ans:

Ans:

Dividing 4 on both sides

(4 ( q+3 ))/(4 ) = 18/4

q + 3 = 9/2 → q = 9/2 – 3 → q = (9-6 )/2

q = 3/2

**ii)– 4 ( m + 3 ) = 16**

**Ans:**Dividing both sides by – 4

(- 4 ( m+3 ))/(- 4 ) = 16/(- 4)

m + 3 = – 4 → m = – 4 – 3 →m = – 7

**iii) 3( t – 4 ) = 27**

**Ans:**Dividing both sides by 3 we get

(3 ( t-4 ))/3 = 27/3

t – 4 = 9 → t = 9 + 4 → t = 13

**iv)–5 ( s – 3 ) = 45**

**Ans:**Dividing both sides by – 5 we get

(- 5 ( s-3 ))/(- 5 ) = 45/(- 5)

s – 3 = – 9 → s = – 9 + 3 → s = – 6

**5) If 5 is added to twice a number, the result is 29. Find the number.**

**Ans:** Let the required number be x

5 added to twice a number gives

2x + 5 = 29

2x = 29 – 5 → 2x = 24 → x = 24/2 → x = 12

Therefore, the required number is 12.

**6) Solve the following equation**

**3 (p – 2) = 2 ( p – 1 ) – 3**

**Ans:** 3 (p – 2) = 2 ( p – 1 ) – 3

3p – 6 = 2p – 2 – 3

3p – 2p = – 2 – 3 + 6

1p = – 5 + 6

p = 1

**7) The sum of three consecutive multiples of 2 is 18. Find the number .**

**Ans:** Let the 1st multiple be x

Therefore, the 2nd multiple is x + 2

“ the 3rd “ is x + 4

x + x + 2 + x + 4 = 18

3x + 6 = 18

3x = 18 – 6

3x = 12 → x = 12/3 → x = 4

**8) Solve:**

**i) 3m/2 = 2/3 (ii) z/5 = 45/25 (iii) t/3 = 4/6**

**i) 3m/2 = 2/3 **

**Ans:**

→ 3m = 2/3 x 2

→ 3m = 4/3

→ m = 4/(3 x 3 )

→ m = 4/9

**ii) z/5 = 45/25**

**Ans:**

→ z = 45/25 x 5

→ z = 45/5

→ z = 9

**iii)t/3 = 4/6**

Ans.

→ t = 4/6 x 3

→ t = 4/2

→ t = 2

**9) Sahil’s father’s age is 5 years more than twice Sahil’s age. Find Sahil’s age, if his father is 47 years old.**

**Ans:** Let Sahil’s age be x

Sahil’s father’s age is 2x + 5

2x + 5 = 47

2x = 47 – 5

2x = 42 → x = 42/2 → x = 21

**10) The length of a rectangle is twice its breadth .if its perimeter is 54cm, find the length and the breadth of the rectangle.**

**Ans:** Let the breadth of the rectangle be y

The length of the rectangle is 2y

Perimeter = 2 ( length + breadth )

= 2 ( 2y + y )

= 2 ( 3y )

= 6y

54 = 6y

54/6 = y → y = 9

Therefore, the breadth is 9cm and the length is 2y = 2 x 9 = 18cm