It's about consecutive odd numbers

Question

Three friends went to a concert where the seats were numbered as consecutive odd numbers. Triple the largest number is two less than the product of 5 and the smallest number. What is the middle seat number? 

 

It's asking for a key, equation and the solution. I tried doing this for about two hours and can't seem to get it.

Answer 1

Let n = the middle number.  Then the 3 consecutive odd numbers are

 

n - 2

n

n + 2,

 

with

 

n - 2 < n < n + 2

 

Triple the largest number:  3(n + 2)

The product of 5 and the smallest number:  5(n - 2)

Two less than the product of 5 and the smallest number:  5(n - 2) - 2

 

Then

 

3(n + 2) = 5(n - 2) - 2

 

Solve for n and get:

 

3n + 6 = 5n - 10 - 2

 

-2n = -18

 

n = 9

 

The three numbers are 7,9,11