Question

The sum of three consecutive even integers is equal to -102. Find three integers:The first (smallest) integer is equal to : The middle integers is equal to : The last (largest) integer is equal to :

Answer 1

we call the first number: x

The next even integer will be: x+2

And the third even integer: x+4

Note: from the first number 2 the second number we add two, because even numbers are 2 numbers apart, for example 2 and 4, 4 and 6, etc.

We are told that the sum of the three numbers is -102, thus, we add the numbers and equal them to -102:

`x+x+2+x+4=-102`

On the left side, we combine like terms:

`3x+6=-102`

Next, we substract 6 from both sides:

`\begin{gathered} 3x+6-6=-102-6 \\ 3x=-108 \end{gathered}`

And now we divide both sides by 3:

`\begin{gathered} (3x)/(3)=(-108)/(3) \\ x=-36 \end{gathered}`

Since we knoe x, we can find the numbers:

First number: x ----> -36

Second number: x+2 ---> -36+2=-34

Third number: x+4 ---> -36+4=-32

Smallest number: -36

Middle number: -34

Largest number: -32