Which expression represents the sum of two consecutive even numbers if the total is 80?

To understand why the expression that represents the sum of two consecutive even numbers, which totals 80, is the one involving (2n + 2 = 80), we first need to define what consecutive even numbers are. Consecutive even numbers can be described in terms of a variable (n).

If we let (n) represent the first even number, the next consecutive even number can be represented as (n + 2). Therefore, the sum of these two consecutive even numbers can be expressed mathematically as:

[ n + (n + 2) = 2n + 2 ]

This expression correctly accounts for both even numbers since it takes the first even number, adds it to the next consecutive even number, and results in a total of (2n + 2).

Given that their total is 80, we can set this equation equal to 80:

[ 2n + 2 = 80 ]

This correctly represents the mathematical relationship we are looking for, leading us to conclude that the given expression indeed represents the sum of the two consecutive even numbers equating to 80.

Other expressions do not accurately capture the relationship between two consecutive even numbers in the same