find 4 consecutive ODD numbers whose sum is equal to 96.

Expert Answers
hala718 eNotes educator| Certified Educator

let us assume the first number is x

then x+(x+2)+(x+4)+(x+6)= 96

==> 4x+12=96

==> 4x= 84

==> x= 21

Then The numbers are: 21, 23, 25, 27

neela | Student

Let the four consecutive ODD numbers be 2x+1, 2x+3 ,2x+5 and 2x+7.

Then their algebraic sum is: (2x+1)+(2x+3)+(2x+5)+(2x+7) which is given to be 96. So,

8x+16 = 96

x+2 = 12. Or

x = 12-2 = 10

Therefore the 4 consecutive odd numbers are = 2*10+1 =21 and then 23, 25, and 27.

Check : 21+23+25+27 =  96

givingiswinning | Student

 x+(x+2)+(x+4)+(x+6)= 96

combine like terms:

4x + 12 = 96

subtract 12

4x = 84

divide by 4

x = 21

21, 23, 25 and 27

atyourservice | Student

 x+(x+2)+(x+4)+(x+6)= 96

combine like terms:

4x + 12 = 96

subtract 12

4x = 84

divide by 4:

x = 21

21 is the lowest number so the numbers should be 21, 23, 25 and 27

Wiggin42 | Student

Odd numbers can be written as 2n + 1

(2n+1) + (2n+3) + (2n+5) + (2n+7) = 96

8n + 16 = 96

8(n + 2) = 96

n + 2 = 12

n = 10 

Therefore, the consecutive odd numbers that add up to 96 are

21, 23, 25, 27,