Find three consecutive even integers such that the sum of twice the first and three times the third is fourteen more than four times the second.

Expert Answers
Seema Adiga eNotes educator| Certified Educator

Let the three even integers be `x, x+2, x+4` (with 2 difference)

According to the question, two times first i.e. `2x` , 3 times the third i.e.

`3(x+4) ` and 4 times the second i.e. `4(x+2)```

`2x + 3(x+4) = 14 + 4(x+2)` 

` `

`2x + 3x + 12 = 14 + 4x + 8`

separate x terms and constants

`2x + 3x - 4x = 14 + 8 - 12`

`x = 10`

`therefore` the required numbers are 10, 12 and 14

lets verify the answer:

`10 + 3*14 = 14 + 4*12`

`52 = 52` 

Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

Any even integer has the form 2*n for some integer n. The next even integer is 2n+2 and the next is 2n+4.

It is given that

2*(2n) + 3*(2n+4) = 4*(2n+2) + 14.

Gather terms with and without n and obtain

10n+12=8n+22,

2n=10,

n=5.

So the first even integer is 10, the second is 12 and the third is 14.