12. find three consecutive even integers such that the sum of the smallest number and twice the middle…

12. find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number.

12. find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number.

Answer

Answer:

Let the three consecutive even integers be (x), (x + 2), (x+4). The sum of the smallest number and twice the middle number is (x+2(x + 2)=x + 2x+4=3x + 4). The largest number is (x + 4). We are given that (3x + 4=(x + 4)+20).

[ \begin{align*} 3x+4&=x + 4+20\ 3x+4&=x+24\ 3x-x&=24 - 4\ 2x&=20\ x&=10 \end{align*} ]

The three consecutive even integers are (10), (12), (14)