Question

The sum of two even consecutive integers is 114. What is the smallest integer?

Answer 1

56

Explanation:

The sum of two even consecutive integers is 114.

Let's let the first even integer be 2n, where n is some integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.

So, this means that the second number is 2n+2.

Their sum is 114. In other words:

`(2n)+(2n+2)=114`

Solve for n.

Combine like terms:

`4n+2=114`

Subtract 2 from both sides:

`4n=112`

Divide both sides by 4:

`n=28`

So, n is 28.

This means that the first number is 28(2) or 56.

And the second number is 58.

So, the smallest integer is 56.

And we're done!