Question

The sum of three consecutive even integers is 180. How do you find the numbers?

Answer 1

Answer: `58,60,62`

Explanation:

Sum of 3 consecutive even integers is 180; find the numbers.

We can start by letting the middle term be `2n` (note that we can't simply use `n` since it would not guarantee even parity)

Since our middle term is `2n`, our other two terms are `2n-2` and `2n+2`. We can now write an equation for this problem!
`(2n-2)+(2n)+(2n+2)=180`

Simplifying, we have:
`6n=180`

So, `n=30`

But we're not done yet. Since our terms are `2n-2,2n,2n+2`, we must substitute back in to find their values:
`2n=2*30=60`
`2n-2=60-2=58`
`2n+2=60+2=62`

Therefore, the three consecutive even integers are `58,60,62`.

Answer 2

`58,60,62`

Explanation:

let the middle even numbe rbe `2n`

the others will then be

`2n-2" and "2n+2`

`:. 2n-2+2n+2n+2=180`

`=>6n=180`

`n=30`

the numbers are

`2n-2=2xx30-2=58`

`2n=2xx30=60`

`2n+2=2xx30+2=62`

Answer 3

see a solution process below;

Explanation:

Let the three consecutive even integers be represented as; `x+2 , x+4, and x+6`

Hence the sum of three consecutive even integers should be; `x+2 + x+4 + x+6 = 180`

Therefore;

`x+2 + x+4 + x+6 = 180`

`3x + 12 = 180`

Subtract `12` from both sides;

`3x + 12 - 12 = 180 - 12`

`3x = 168`

Divide both sides by `3`

`(3x)/3 = 168/3`

`(cancel3x)/cancel3 = 168/3`

`x = 56`

Hence the three consecutive numbers are;

`x + 2 = 56 + 2 = 58`

`x + 4 = 56 + 4 = 60`

`x + 6 = 56 + 6 = 62`