Find three consecutive odd integers such that the sum of the first and third equals the sum of the second and 33.

31, 33, 35

Explanation:
We can set the variable for the first integer of the three consecutive integers as x.

First integer=x

Because they are all odd, we can then say that the second integer is equal to the first integer plus 2.

Second integer=x+2

Using the same knowledge, we can say that the third integer is equal to the second integer plus 2.

Third integer=x+2+2
Third integer=x+4.

Now, we have our three integers:
First integer=x
Second integer=x+2
Third integer=x+4

We can write out equation out like this:
(x)+(x+4)=(x+2)+33
The sum of the first (x) and third (x+4) integers is equal to the sum of the second (x+2) and 33.

Now, we solve this equation.
(x)+(x+4)=(x+2)+33
Open up the parentheses
x+x+4=x+2+33
Combine like terms
2x+4=x+35
Subtract both sides by 4
2x+4-4=x+35-4
2x=x+31
Subtract both sides by x
2x-x=x+31-x
x=31

Now, we know that our first integer is 31. Because these integers are consecutive and odd, we know that our second integer is 33 and the third is 35.

I hope this helps!

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