How do you find two consecutive even integers that have a sum of 450?

May 19, 2016

The two numbers are $224 \text{ and } 226$

Explanation:

Let the first even number be $n$

Then the next number is $n + 1$ which is odd.
Then the number after that is $n + 2$ which is even.

So the two even number are $n \text{ and } n + 2$

We are given that $n + n + 2 = 450$

Subtract 2 from both sides

$2 n = 448$

Divide both sides by 2

$n = 224$

$\implies n + 2 = 226$

So $\text{Left Hand side } \to 224 + 226 \to 450$

So LHS -> RHS thus the two numbers are $224 \text{ and } 226$