The sum of four consecutive odd integers is three more than 5 times the least of the integers, what are the integers?

Question

2568 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-20T11:54:04

$n->{9,11,13,15}$

$color(blue)("Building the equations")$

Let the first odd term be n
Let the sum of all the terms be s

Then
term 1 $->n$
term 2 $->n+2$
term 3 $->n+4$
term 4 $->n+6$

Then
$s=4n+12$ .................................(1)

Given that

$s=3+5n$ ..................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equating (1) to (2) thus removing the variable s

$4n+12=s=3+5n$

Collecting like terms

$5n-4n=12-3$

$n=9$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus the terms are:

term 1 $->n->9$
term 2 $->n+2->11$
term 3 $->n+4->13$
term 4 $->n+6->15$

$n->{9,11,13,15}$