Five consecutive integers add up to 85. What are the numbers?

Question

6623 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-01T23:01:49

The five consecutive integers are $15, 16, 17, 18, 19$

To identify five consecutive integers we begin by giving them each a variable expression

$1st = x$
$2nd = x+ 1$
$3rd=x+2$
$4th = x+3$
$5th = x+4$

Now we set these equal to a sum of 85

$x + x + 1 + x + 2 + x + 3 + x + 4 = 85$

$5x + 10 = 85$

$5x cancel(+ 10) cancel(- 10)= 85 - 10$

$5x = 75$

$(cancel5x)/cancel5 = 75/5$

$x = 15$

$1st = x = 15$
$2nd = x+ 1=16$
$3rd=x+2=17$
$4th = x+3=18$
$5th = x+4=19$

Answer 2 · 2016-06-01T23:13:08

$15, 16, 17, 18, 19$

If the middle integer is $n$ , then we are given:

$85 = (n-2)+(n-1)+n+(n+1)+(n+2) = 5n$

Divide both ends by $5$ and transpose to find:

$n = 17$

So the five integers are:

$15, 16, 17, 18, 19$