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

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Answer 1 · 2016-11-27T08:58:19

See 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 · 2016-11-27T09:01:21

14, 16, 18

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:
$14+16+18 = 48$
$48 = 18+30$