Algebra Homework Help?

Question

Here is the problem:

Find three consecutive even numbers whose sum is 468.

I know it probably seems simple, but I don't really understand.
Help?

Please & Thank you all!

Answer 1

Your question is an arithmetic sequence topic.

Follow the step below:

Firstly, write the term:
T (1) = x - 2
T (2) = x
T (3) = x + 2
So, T (sum) = 468

Then, we know that T (1) + T (2) + T (3) = T (sum)
So, (x - 2) + (x) + (x + 2) = 468

Next, solve the equation:
x - 2 + x + x + 2 = 468
3x = 468
x = 156

Then,
T (1) = x - 2
T (1) = 156 - 2
T (1) = 154
T (2) = x
T (2) = 156
T (3) = x + 2
T (3) = 156 + 2
T (3) = 158

Therefore, three consecutive even numbers whose sum is 468 are 154, 156, and 158.

Answer 2

Let the first even integer be n
Let the second even integer be n + 2
Let the third even integer be n + 4

Add these up:
n + n + 2 + n + 4 = 468

3n + 6 = 468
3n = 462
n = 154

So the numbers are 154, 156, 158

Answer 3

let three consecutive even numbers be

2n, 2n+2 and 2n +4

The reason i used 2n instead of n is that
2n is always even for any value of n, whereas an arbitrary n can be either odd or even ( it's not general)

2n +2n+2 +2n+4 = 6n +6 = 468
6n = 462
n = 462/6 =77

the 3 numbers are
2n = 154 ;
2n+2 = 156 and
2n +6 =158

Answer 4

154, 156, and 158.
you divide the number you have into 3. the answer you get is the 2nd number. then you just subtract 2 to get your first number, and you add 2 to get your 3rd number.