Question

Find three consecutive even integers such that the sum of the second and third is 3 times the first integer.

Answer 1

`6`,
`8` and
`10`

Explanation:

Let
`x =` smallest consecutive even integer.

Since the second and third consecutive even integers can be expressed by our smallest even consecutive integer, we can express them as:

Second consecutive even integer =
`x+2`

Third consecutive even integer =
`x+4`

From "the sum of the second and third is 3 times the first integer", we can write:

`x+2+x+4 = 3x`

`2x+6 = 3x` (collect like-terms)

`x=6`

∴ The first consecutive even integer is 6

Now, we can use substitution to find the values of the second and third consecutive even integers:

Second consecutive integer =
`x+2`

`=6+2`

`=8`

Third consecutive integer =
`x+4`

`=6+4`

`=10`

∴ The three consecutive even integers are
`6`,
`8` and
`10`.

Hope this helps :)