# How do you find three consecutive odd integers such that when five times the third minus the second is added to the first, the result is 23?

May 23, 2018

The three odd numbers are color(purple)(1,3,5

#### Explanation:

Let the three numbers be $a , b , c$

$c = b + 2 , c = a + 4 , b = a + 2$

Given : $5 c - b + c = 23$

Substituting values of a & b in terms of c,

$5 c - \left(c - 2\right) + \left(c - 4\right) = 23$

$5 c - \cancel{c} + 2 + \cancel{c} - 4 = 23$

$5 c = 23 + 4 - 2 = 25$

$c = \frac{25}{5} = 5$

$b = c - 2 = 3 , a = c - 4 = 1$