Question

7) Six added to twice of a whole number gives 32. Find the
whole number.

8) The sum of three consecutive natural numbers is 54. Find
the numbers.

9) The length of a rectangle is 9 cm more than its breadth. If its
perimeter is 66 cm, find the length and breadth.
10) The difference between two numbers is 8. Ten times the
smaller plus the larger is 41. Find the numbers.
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Answer 1

Answer:

7) 13

8) 17

9) Length = 33cm

Breadth = 24 cm

10) Smaller number = 3

Larger number = 11

Explanation:

7) let the no. = x

sum = 32

Therefore

2x + 6 = 32

2x = 32 - 6

2x = 26

x = 26/2

x = 13

Number = 13

8) let 1st number = x

2nd number = x+1

3rd number = x+ 2

Total sum = 54

Therefore

x + x + 1 x + 2 = 54

3x + 3 = 54

3x = 54 - 3

3x = 51

x = 51/3

x = 17

1st number = 17

2nd number = 17 + 1 = 18

3rd number = 17 + 2 = 19

9) let the breadth = x cm

length = x + 9 cm

perimeter = 66 cm

Therefore

2 ( x + 9 + x ) = 66

2 ( 2x + 9 ) = 66

4x + 18 = 66

4x = 66 - 18

4x = 48

x = 48/4

x = 24

Length = 24 + 9 = 33cm

Breadth = 24cm

10) let the smaller number = x

bigger number = x + 8

total sum = 41

ten times the smaller no. i.e. 10x

According to question

10x + x + 8 = 41

11x + 8 = 41

11x = 41 - 8

11x = 33

x = 33/11

x = 3

Smaller number = 3

Bigger number = 3 + 8 = 11