# How do you find the two integers if the sum of two consecutive odd integers is 40?

Mar 25, 2015

Two consecutive odd numbers can be written:

${n}_{1} = 2 k - 1$
${n}_{2} = 2 k + 1$

Than:

$2 k - 1 + 2 k + 1 = 40 \Rightarrow 4 k = 40 \Rightarrow k = 10$,

So:

${n}_{1} = 2 k - 1 = 19$
${n}_{2} = 2 k + 1 = 21$.

Mar 25, 2015

If the smaller odd number is $n$, then the next consecutive odd number is $n + 2$

$\left(n\right) + \left(n + 2\right) = 40$

$\rightarrow 2 n + 2 = 40$

$\rightarrow 2 n = 38$

$\rightarrow n = 19$

So the two integers are $19$ and $21$