Question

The sum of three consecutive even integers is 30 more than the largest. What are the integers?

Answer 1

See explanation.

Explanation:

First we have to write the given data in mathematical terms.

The three consecutive even numbers can be written as `2n`, `2n+2` and `2n+4`.

From the first sentence of the task we can deduce that the sum of `2n` and `2n+2` is `30`.

`2n+2n+2=30`

`4n+2=30`

`4n=28`

`n=7`

Now we can calculate the numbers and write the answer:

`2n=14`; `2n+2=16` and `2n+4=18`

Answer: The numbers are: 14, 16 and 18

Answer 2

14, 16, 18

Explanation:

Let `n` be the smallest positive integer in the sequence

Hence the sum on the three even integers is: `n+ (n +2) + (n+4)`

We are told that this sum is 30 more than the largest which must be `(n+4)`

`:. n+ (n +2) + (n+4) = 30 + (n+4)`

`3n+6 = n+34`

`2n=28`

`n=14`

Hence the sequence is: 14, 16, 18

To check:
`14+16+18 = 48`
`48 = 18+30`