# How do you find all sets of three consecutive even integers whose sum is between 25 and 45?

##### 1 Answer

Mar 12, 2016

solutions are: 8 10 12

or 10,12,14

or 12,14,16

#### Explanation:

Let the first even number be n. The sum will be n+n+2+n+4=3 n + 6 and

25 < 3 n + 6 < 45.

19<3n<39

So,

possible values of n = 8,10,12

For the starter n = 8, the sum is 8 + 10 +12 = 30.

for n= 10 there exists thee numbers 10.12,14,where sum =36

for n= 12 there exists thee numbers 12,14,16,where sum =42

Hence sets of three consecutive numbers are

set1

or

set2

or

set3