Question

If the sum of three consecutive even integers is 66 what are the integers?

Answer 1

`20, 22, 24`

Explanation:

Take the first integer as `x`. Since we are talking about the next even integer, it will come when you add two to `x`.

For example, let's say that you have `2` as the value of `x`. The next even integer is `4`, which is `x+2`, and the next is `6`, which is `x+4`.

So eventually, the equation is

`(x)+(x+2)+(x+4) = 66`

`3x + 6 = 66`

`3x = 66-6`

`3x = 60`

`x = 60 ÷ 3`

`x = 20`

So

• `x = 20`
• `x+2 = 22`
• `x+4 = 24`

Answer 2

So the three numbers are: `20; 22; 24`

Explanation:

You have to 'jump' an odd number to get to the next even number. So even numbers occur every second place (counting in 2's)

Set the first even number as `n`
Then the second is `n+2`
The third is `n+4`

`(n)+(n+2)+(n+4) = 3n+6 = 66`

Subtract 6 from both sides

`3n=60`

Divide both sides by 3

`n=20`

So the three numbers are: `20; 22; 24`

Answer 3

Let us assume the first even number to be `color(purple)(x`.

So the other to Consecutive even numbers would be:

`color(purple)(x+2 and x+4.`

So, according to the question,

`color(green)(->(x)+(x+2)+(x+4)=66`

`->x+x+x+2+4=66`

`->3x+6=66`

`->3x+cancel6-cancel6=66-6`

`->3x=60`

`(cancel(3)x)/cancel3=60/3`

`color(magenta)(x=20`

And so, the three consecutive even numbers which sum up to 66 :

`color(red)(1. x=20`

`color(red)(2. x+2=22`

`color(red)(3. x+4=24`

As a check:

The sum of all three should be `66`

`color(blue)(=20+22+24`

`color(blue)(=66`

Hence it is proved that the 3 no.s are `color(Darkorange)(20, 22 and 24`

~Hope this helps! :)