Question

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?

Answer 1

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.