Question

3 consecutive even integers whose sum is 54

Answer 1

The answer is 16, 18, and 20

Here's how we find that out:

First we have to know what consecutive integers are: When you have a group of consecutive integers, the mean (average of all the numbers) and the median ( middle number after all the numbers are placed from least to greatest) must be equal. 

Correct consecutive integers:

- 1, 3, 5, 7, 9

- 2, 4, 6

- 7, 9, 11

Incorrect consecutive integers:

- 1, 3, 5, 7

- 2, 4, 6, 8

- 11, 13

Now that we know how consecutive integers work, we can set up an equation and solve for our answer:

$x+(x+2)+(x+4)=54$

The reason this is our equation is because if we look at it, we are using x as our first integer, that way once we find our first consecutive integers, the next two require no more math to find. This is an example of why our equaion looks like it does:

Let's say we had our three consecutive integers of 2, 4, and 6 that add up to 12. In our case, 2 will be the x in our equation.

$x+(x+2)+(x+4)=12$
$x+(4)+(6)=12$

That is how our equation will work. Now to put it to use to our problem and simplify it until we find our first integer:

$x+(x+2)+(x+4)=54$............................Combine our like terms 

$3x+6=54$..........................................Subtract 6 from both sides

$3x=54-6$...........................................Simplify

$3x=48$..............................................Divide both sides by 3

$x=16$................................................First Integer!

Now that we know our first integer, we just plug it into our equation and find the other two! :)

$16+(16+2)+(16+4)=54$

$16+(18)+(20)=54$

$54=54$

And there you have it. Our three integers are: 16, 18, and 20

Thank you for your question! I hope this helped! Have an amazing day and feel free to let me know if you have any further questions! :D

Answer 2

N+n+2+n+4=54

3n+6=54

3n=48

n=16

16, 18, 20