Math, asked by sondersourabh96, 8 days ago

The sum of 5 consecutive integers is 35. how many of the five consecutive integers are prime numbers​

Answers

Answered by shaswatraj2008
1

Answer:

Step-by-step explanation:

Let the consecutive integers be.

x+x+1+x+2+x+3+x+4=35

5x+10=35

5x=35-10

5x=25

x=25/5

x=5.

The consecutive integers are.

x=5, x+1=6,x+2=7,x+3=8,x+4=9.

In this 5 and 7 are prime numbers.

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Answered by divyapakhare468
0

To find : five consecutive integers and how many of the five consecutive integers are prime numbers​ .

Given : The sum of 5 consecutive integers is 35 .

Solution :

  • As per given data we know that the sum of 5 consecutive integers is .  
  • We know that consecutive integers differ by 1 .
  • Therefore , let x, x+ 1 , x + 2 , x+ 3 , x + 4 be the  5 consecutive integers.
  • According to given condition we write as , x + x + 1 + x + 2 + x + 3 +x +4 = 35
  • Using transposition method we find the value of x , by leaving variable at LHS and transposing constants at RHS .
  • x + x + 1 + x + 2 + x + 3 +x +4 = 35  

        5x  +10= 35 \\ 5x = 35 - 10 \\ 5x = 25 \\ x= \frac{25}{5} \\ x= 5

  • Now , consecutive numbers are :

       x = 5 \\x + 1 = 5 + 1 = 6 \\ x + 2 = 5 + 2 = 7 \\ x + 3 = 5 + 3 = 8\\x  + 4 = 5 + 4 = 9

  • Prime numbers are the numbers having only two factors 1 and number itself .
  • Now , prime numbers​ among obtained consecutive numbers are : 5 and 7 .  

Hence ,  five consecutive integers are 5,6,7,8, 9 .There are two consecutive integers that are prime numbers​ they are 5 and 7 .

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