# Twice the greater of two consecutive odd integers is 13 less than three times the lesser, how do you find the integers?

Aug 4, 2015

The integers are $17$ and $19$.

#### Explanation:

The trick when dealing with consecutive numbers of any kind is to use the smallest one to express the others.

In your case, if $x$ is an odd number, the consecutive odd number will be $\left(x + 2\right)$, since $\left(x + 1\right)$ would be an even number.

So, you know that if you double the bigger of the two numbers and add $13$ to the result, you get a number that's three times larger than the smaller of the two numbers.

This is equivalent to saying that

$2 \cdot {\underbrace{\left(x + 2\right)}}_{\textcolor{b l u e}{\text{bigger number")) + 13 = 3 * underbrace(x)_(color(green)("smaller number}}}$

This means that you have

$2 \left(x + 2\right) + 13 = 3 x$

$2 x + 4 + 13 = 3 x \implies x = \textcolor{g r e e n}{17}$

The bigger number will be

$x + 2 = 17 + 2 = \textcolor{g r e e n}{19}$