Question 209881
Let the middle number is n. 
Then the three numbers can be expressed as n-2,n,n+2.

Their sum is n-2 + n + n + 2 = 3n.

Now use the given relationship to set up an equation:
twice their sum is 30 less than 8 times the third integer


The relationship can be written as:
2* their sum = 8*the third number - 30

2*3n =8(n+2)-30
Solving for n, we have
6n = 8n + 16 -30
0 = 2n - 14
2n = 14
n = 7
So the three numbers are 5, 7, 9.