Question

If the sum of 3 consecutive even integers is 30 how do you find the numbers?

Answer 1

The three numbers are 9, 10, and 11

Explanation:

Let `n` be the smallest of the three consecutive numbers
`rarr` the other two numbers are `n+1` and `n+2`

We are told
`color(white)("XXX")(n) + (n+1) + (n+2) = 30`

`rarr color(white)("XX")3n+ 3 = 30`

`rarr color(white)("XX")3n = 27`

`rarr color(white)("XX")n = 9`

Answer 2

`8`, `10` and `12`

Explanation:

We can define an even number as `2x`

Let `2x` be the first even number

Let `2x+2` be the next even number

Let `2x+4` be the last one

Their sum is `30` so we write

`2x+(2x+2)+(2x+4)=30`

Combining like terms

`6x+6=30`

`6x=24`

`x=4`

So

`2x=2(4)=8`

`2x+2=8+2=10`

`2x+4=8+4=12`