# Question #1ea10

Oct 15, 2017

$68 , 70 , 72$

#### 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:

$\left(x\right) + \left(x - 2\right) + \left(x + 2\right) = 210$

$3 x = 210$

$x = 70$

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 $68 + 70 + 72 = 210$.

Oct 15, 2017

Any two numbers from the set $\left\{68 , 70 , 72\right\}$

#### Explanation:

Any number is even when it is doubled, so $e = 2 n , n \in \mathbb{Z}$

So, a set of even numbers will be $E = \left\{2 n , 2 n + 2 , 2 n + 4 , \setminus \cdots\right\}$

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

$6 \left(n + 1\right) = 210$

$n + 1 = \frac{210}{6} = 35$

$n = 35 - 1 = 34$

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

Oct 15, 2017

$68 , 70 , 72$

#### Explanation:

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

$x + \left(x + 2\right) + \left(x + 4\right) = 210 \to \text{Statement}$

Solving..

$x + x + 2 + x + 4 = 210$

$3 x + 6 = 210$

$3 x = 210 - 4$

$3 x = 204$

$x = \frac{204}{3}$

$x = 68$

Hence

The numbers are

$x = 68$,

$x + 2 = 70$

$x + 4 = 72$