Question

The sum of three consecutive even integers is six more than two times the smallest integer. Find all the integers.

Answer 1

Let "x" be the smallest integer

this would mean the next even integer can be described by "x+2"
what would the next integer be represented as?

Answer 2

write even integers as 2k

Answer 3

three consecutive even numbers would be 2k, 2(k+1), 2(k+2)

Answer 4

see if you can use that to try and write an equation from the statement you are given

Answer 5

and solve for k

Answer 6

I would suggest something more along the lines of the strategy that @completeidiot was using.

Answer 7

For example, three consec. even entegers: 2, 4, 6
If you let x be the smallest of the three integers: x = 2
then you can get to the next number by adding 2 to x : x+2 = 2+2 = 4
and then the last number is just x+4: x+4 = 2+4 = 6

Answer 8

Of course the number 2,4,6 is not the actual answer to your question, but small cases like this may help you understand the problem.

Answer 9

Question: The sum of three consecutive even integers is six more than two times the smallest integer.
Translate: x + (x+2) + (x+4) = 2x+6

Answer 10

@cruffo no, specifying a number as 'x' doesn't guarantee that it will be even.

Answer 11

that's why you use 2k, 2(k+1), etc.

Answer 12

@Algebraic!, I understand what you are saying by "2k". Your method will also work. However, it is not actually necessary for these types of number problems.

Answer 13

In your method, you get
2k + 2(k+1) + 2(k+2) = 2(2k) + 6
and you can divide out all the 2's

Answer 14

then you get
k + k+1 + k+2 = 2k + 3

Answer 15

However solving for k won't give you the smallest integer. after you solve for k, you'll need to go back and multiply k by 2 to get the final answer.

Answer 16

Actually, I don't think you actually get an answer by doing that:
3k + 3 = 2k+3
k=0???

Answer 17

yep

Answer 18

ask cruffo then. the problem is already done, however.