Question

Two consecutive even numbers whoes sum is 126

Answer 1

Since an even number can be represented as:

`2n`

With n a natural number, and the next even number is:

`2n+2`

Set the sum of both even numbers equal to 126:

`(2n)+(2n+2)=126`

Solve for n:

`\begin{gathered} \Rightarrow2n+2n+2=126 \\ \Rightarrow4n+2=126 \\ \Rightarrow4n=126-2 \\ \Rightarrow4n=124 \\ \Rightarrow n=(124)/(4) \\ \Rightarrow n=31 \end{gathered}`

Substitute back n=31 into the expressions for the even numbers to find them:

`\begin{gathered} 2(31)=62 \\ 2(31)+2=64 \end{gathered}`

Therefore, the two consecutive even numbers whose sum is 126, are 62 and 64.