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:

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