Consecutive Odd Integers

[Kandis]

What is the largest of three consecutive odd integers if the product of the first and third integers is 6 more than 3 times the second integer?

 

[galactus]

Here is one way to tackle it.

Designate your first odd as 2x+1. The second odd would then be 2x+3, the third would be 2x+5.

The product of the first and third: (2x+1)(2x+5)

Is 6 more than 3 times the second 3(2x+3)+6

Equate them and solve for x. Then, sub it into 2x+1 to see what the first one is.

Since they are consecutive, it is easy to see what the other two will be.

Check to see if they meet the requirements.

 

[Loren]

What is the largest of three consecutive odd integers if the product of the first and third integers is 6 more than 3 times the second integer?

Galctus named one of the three numbers "2x+1". This designation assures you that the number is odd. However you could call the three numbers n, n+2 and n+4 and it would work just as good. In this case you will get two results, one being an odd integer and the other an even integer. By the wording of the question, you know which one to pick.