# How do you find three consecutive odd integers such that the sum of the first and second is 27 less than three times the third?

Apr 28, 2016

Another method

The numbers are $17 , 19 , 21$

#### Explanation:

Let the first odd number be $n$

Breaking the question down into its key parts

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Three consecutive odd number$\to n \text{ ; "n+2" ; } n + 4$

Sum of first and second numbers:$\to n + n + 2$

Is:$\to n + n + 2 =$

27 less:->n+n+2=?-27

than three times the third:$\to n + n + 2 = 3 \left(n + 4\right) - 27$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\implies 2 n + 2 = 3 n + 12 - 27$

$\implies 2 n + 2 = 3 n - 15$

$\implies 3 n - 2 n = 2 + 15$

$\implies n = 17$

The numbers are $17 , 19 , 21$