The sum of 5 consecutive odd integer is 685. What are the numbers
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Answered by
9
Answer:
Numbers, required here, are 133 , 135 , 137 , 139 and 141.
Step-by-step explanation:
Let the required consecutive odd integers are 2a - 5 , 2a - 3 , 2a - 1 , 2a + 1 , 2a + 3
According to the question : -
⇒ Sum of 5 consecutive odd integers = 685
= > ( 2a - 5 ) + ( 2a - 3 ) + ( 2a - 1 ) + ( 2a + 1 ) + ( 2a + 3 ) = 685
= > 2a - 5 + 2a - 3 + 2a - 1 + 2a + 1 + 2a + 3 = 685
= > 2a + 2a + 2a + 2a + 2a - 5 - 1 + 1 - 3 + 3 = 685
= > 10a - 5 = 685
= > 10a = 685 + 5
= > 10a = 690
= > a = 690 / 10
= > a = 69
Therefore, required consecutive odd numbers are : -
2a - 5 = 2( 69 ) - 5 = 138 - 5 = 133
2a - 3 = 138 - 3 = 135
2a - 1 = 138 - 1 = 137
2a + 1 = 138 + 1 = 139
2a + 3 = 138 + 3 = 141
Required numbers are 133 , 135 , 137 , 139 , 141.
Answered by
8
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Let first odd integer be x
•°• Second consecutive odd integer be x+2
•°•Third consecutive odd integer be x+4
•°•Fourth consecutive odd integer be x+6
•°• and Fifth consecutive odd integer be x+8
Given that,
=> sum of the five consecutive odd integer =685
=>x+x+2+x+4+x+6+x+8=685
=>5x+ 20=685
=>5x. = 685-20
=>5x. = 665
=>x. = 133
So, we get the first odd integer => x = 133
Now,
Second consecutive odd integer = x+2=133+2=135
•°•Third consecutive odd integer = x+4=133+4=137
•°•Fourth consecutive odd integer =x+6=133+6=139
•°• and Fifth consecutive odd integer = x+8=133+141
Hence,
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