If the sum of the first two of the five consecutive odd integers is 52, what is the sum of the last two integers?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the five odd integers be:

x , x+2 , x+4, x+6 , x+ 8

Then given the sum of the first two integers is 52

==> x + (x+ 2) = 52

Let us combine like terms:

x + x + 2 = 52

==> 2x + 2 = 52

==> 2x = 50

==> x = 25

Then the first number is 25

Then the second numbers is 25+2 = 27

The third consecutive integer = 25+ 4 = 29

The fourth integer is  = 25+ 6) = 31

The fifth integer is = 25+8 = 33

Then the sum of the last two integers is:

 31 + 33 = 64

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The sum of the two odd numbers is 52.

The consecutive odd numbers  has  always the difference 2.

So if x is an odd number x+2 is also an odd number.

So  the sum of the assumed consecutive odd numbers = x+x+2 = 2x+2 which is equal to 52.

Therefore 2x+2 = 52.

So 2x = 52-2 = 50.

Therefore x x= 50/2 = 25.

Therefore the consecutive odd numbers are 25 and 27 whose sum is 52.

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