Question

Question #1ea10

Answer 1

`68,70,72`

Explanation:

I'm not sure what you mean by "find two numbers". I'll just show you how to get all three and hopefully you can get your answer from that.

Let's let `x` be the middle of the three even integers. Then the even integer less than `x` has to be `x-2` and the one above has to be `x+2` because the even integers are consecutive.

We know that the sum is `210`. Thus:

`(x)+(x-2)+(x+2)=210`

`3x=210`

`x=70`

Thus, our middle even integer is `70`. The other even integers are `70-2=68` and `70+2=72`.

As we can see, `68,70,72` are consecutive even integers and `68+70+72=210`.

Answer 2

Any two numbers from the set `{68,70,72}`

Explanation:

Any number is even when it is doubled, so `e=2n, ninZZ`

So, a set of even numbers will be `E={2n,2n+2,2n+4,\cdots}`

Three consecutive numbers that add up to 210 will follow the formula:
`210=2n+2n+2+2n+4=6n+6`

`6(n+1)=210`

`n+1=210/6=35`

`n=35-1=34`

The three consecutive numbers that add up to 210 are `{2(34),2(34)+2,2(24)+4}={68,70,72}`

Answer 3

`68, 70, 72`

Explanation:

Let the consecutive numbers be `x, x+2, x+4`

`x + (x+2) + (x+4) = 210 -> "Statement"`

Solving..

`x + x + 2 + x + 4 = 210`

`3x + 6 = 210`

`3x = 210 - 4`

`3x = 204`

`x = 204/3`

`x = 68`

Hence

The numbers are

`x = 68`,

`x + 2 = 70`

`x + 4 = 72`