How do you find three consecutive odd integers such that the sum of the first and third equals the sum of the second and 25?

1 Answer
Jun 29, 2016

The three consecutive odd integers are 23, 25, 27.

Explanation:

Let #x# be the first odd integer
So,
#x+2# is the second odd integer
#x+4# is the third odd integer

Let's us translate the given expression into algebraic expression:
sum of the first and the third integer equals the sum of the second and 25
that means :
if we add the first and third integer that is :#x+(x+4)#
equals to the sum of the second and 25:# =(x+2)+25#

The equation will be stated as:

#x+x+4=x+2+25#
#2x+4=x+27#
Solving the equation we have:
#2x-x=27-4#
#x=23#

So the first odd integer is 23
The second integer will be #x+2=25#
The third integer is #x+4=27#

So the three consecutive odd integers are:23 ,25 ,27.