Question

(Before you answer I am looking for how I do it. I have the answers but I need to know an equation to do this instead of using logic)

The sum of two consecutive even numbers is 30. How can you solve for the 2 numbers?

Answer 1

14 and 16.

Explanation:

We know that two consecutive even numbers is 30.

Let's let n be any number.

Then the first even number must be 2n.

This is because n can be any number, either even or odd. However, if we multiply it by 2, this ensures that 2n is even. Remember that any number multiplied by 2 yields an even number.

Therefore, the consecutive even number will be (2n+2). Not (2n+1), because that gives an odd number.

We know that they sum to 30. So, we can write the following equation.

`(2n)+(2n+2)=30`

And we solve from there:

`4n+2=30\\\Rightarrow4n=28\\\Rightarrow n=7`

So, the value of n is 7.

Therefore, the first even number is 7(2)=14.

And the consecutive even number is 16.

Edit: Typo