Question

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

Answer 1

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, `19/3 < n < 39/3`.
`=>6 1/3 < n < 13` As n is an even integer,
`8 <= n <=12`
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 `=>8,10,12`
or
set2`=>10,12,14`
or
set3 `=>12,14,16`