Question

The sum of two even integers is 98. What are they? Set up an equation to model the situation. Use the variable n for the value of the smaller integer. SHOW YOUR WORK.

Answer 1

This could have numerous answers because your question does not specify what relationship the two even integers have

Explanation:

Some examples would be 46 and 52, 40 and 58, etc.

However, many of these questions actually state that the two even integers are consecutive (consecutive numbers follow one right after another, such as 52 and 53- even/odd consecutive numbers are even/odd numbers that follow after each other, such as 52 and 54).

If you set up an equation with 2 consecutive numbers it would look something like n+n+2=98. N is the smaller number, and the larger number would be the even number following right after.

Solve the equation:

`2n+2=98 rarr` Combine like terms

`2n=96 rarr` Subtract 2 from each side

`n=48` Divide each side by 2

Thus, the two numbers would be 48 and 50.

Answer 2

`48` and `50`

Explanation:

Let the smaller integer be `n` and the next integer be `n+2`

(`2` is added to `n` to get the consecutive integer)

Now, its given that sum of the two consecutive integers is 98 and it can be written in equation as:

`n + (n+2)` = `98`

or, `2n+2` = `98`

or, 2n = `98-2`

or, `2n` = `96`

or `n` = `cancel96^48/cancel2^1` = `48`

Therefore, `n+2` = `48+2` = `50`