3. (1)
(ii) Find three consecutive odd numbers whose sum is 93.
(iii) Find three consecutive even numbers whose sum is 246.
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Answers
Step-by-step explanation:
1.
Given:
The sum of three consecutive odd numbers is 93
To Find:
The three consecutive odd numbers
Solution:
Let the three odd consecutive numbers be x , x+2 and x+4
Now given is the sum of x , x+2 and x+4 is 93. So, x , x+2 and x+4 is equal to 93.
ACQ,
x+x+2+x+4=93
3x+6=93
3x=93-6
3x=87
x=29
1 st number=29
2nd number=x+2=29+2=31
3rd number=x+4=29+4=33
So, three consecutive odd numbers=29,31 and 33
2.
Given:
The sum of three consecutive even number
To Find:
The three consecutive even numbers
Solution:
Let the three consecutive even numbers be x,x+2,x+4
Given is that the sum of x,x+2,x+4 is 246. So, x,x+2,x+4 is equal to x,x+2,x+4.
ACQ
x,x+2,x+4=246
3x+6=246
3x=246-6=240
3x=240
x=80
1st number=x=80
2nd number = x+2=80+2=82
3rd number = x+4=80+4=84
So the three consecutive even numbers=80,82,84
Question:
- Find three consecutive odd numbers whose sum is 93.
Given that:
- Sum of three consecutive odd numbers is 93.
Let us assume:
- Three consecutive odd numbers be (2x + 1), (2x + 3) and (2x + 5).
According to the question.
↣ (2x + 1) + (2x + 3) + (2x + 5) = 93
↣ 2x + 1 + 2x + 3 + 2x + 5 = 93
↣ 6x + 9 = 93
↣ 6x = 93 - 9
↣ 6x = 84
↣ 3(2x) = 84
↣ 2x = 84/3
↣ 2x = 28
Three consecutive odd numbers:
- 2x + 1 = 28 + 1 = 29
- 2x + 3 = 28 + 3 = 31
- 2x + 5 = 28 + 5 = 33
Hence,
- Three consecutive odd numbers are 29, 31 and 33.
Question:
- Find three consecutive even numbers whose sum is 246.
Given that:
- Sum of three consecutive even numbers is 246.
Let us assume:
- Three consecutive even numbers be 2x, (2x + 2) and (2x + 4).
According to the question.
↠ 2x + (2x + 2) + (2x + 4) = 246
↠ 2x + 2x + 2 + 2x + 4 = 246
↠ 6x + 6 = 246
↠ 6x = 246 - 6
↠ 6x = 240
↠ 3(2x) = 240
↠ 2x = 240/3
↠ 2x = 80
Three consecutive even numbers:
- 2x = 80
- 2x + 2 = 80 + 2 = 82
- 2x + 4 = 80 + 4 = 84
Hence,
- Three consecutive even numbers are 80, 82 and 84.