# Question #1f851

Feb 11, 2017

The greatest number of the three consecutive odd integers whose sum is 81 is $\textcolor{red}{29}$

#### Explanation:

Let's call the first of the three consecutive odd integers $x$. Then, by definition of "consecutive" and "odd" the other two numbers will be $x + 2$ and $x + 4$.

The sum of these three numbers is $81$ so we can write:

$x + x + 2 + x + 4 = 81$

$3 x + 6 = 81$

$3 x + 6 - \textcolor{red}{6} = 81 - \textcolor{red}{6}$

$3 x + 0 = 75$

$3 x = 75$

$\frac{3 x}{\textcolor{red}{3}} = \frac{75}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = 25$

$x = 25$, this is the first integer.

The other two odd integers are:

$x + 2 = 25 + 2 = 27$

$x + 4 = 25 + 4 = 29$