Question

Two consecutive even integers are such that the smaller added to three times the larger is `54`. What are the integers?

Answer 1

`12` and `14`

Explanation:

Since the sum is positive and larger than `6`, we can tell that the integers are both positive. So "larger" is synonymous with "greater" for these two integers.

Let the greater integer be denoted by `n` and the smaller by `n-2`.

Then:

`(n-2)+3n = 54`

Adding `2` to both sides and combining terms, this becomes:

`4n = 56`

Dividing both sides by `4`, this becomes:

`n = 14`

So the two integers are `12` and `14`.

Answer 2

`12 and 14`

Explanation:

Let `x=`the smaller number so `x+2=`the bigger number

It says that `x+3(x+2)=54`

Distribute:

`x+3x+6=54`

Combine like terms:

`4x+6=54`

Subtract 6 and then divide by 4:

`4x=48->x=12`

So our two even numbers are `12 and 14`