Question 107796
Not possible.

consecutive even integers:
2, 4, 6, 8, 10, ....


two consecutive even integers:  
2 and 4

the smaller of the two consecutive even integers (2) is added to 3 times the larger (4) the result is 31. 
2+4(3)=31
2+12=31
14=31 false


two consecutive even integers:  
4 and 6

the smaller of the two consecutive even integers (4) is added to 3 times the larger (6) the result is 31
4+6(3)=31
4+18=31
22=31  false


two consecutive even integers:
6 and 8

the smaller of the two consecutive even integers (6) is added to 3 times the larger (8)  the result is 31
6+8(3)=31
6+24=31
30=31  false


two consecutive even intergers:
8 and 10

the smaller of the two consecutive even integers (8) is added to 3 times the larger (10)  the result is 31
8+10(3)=31
8+30=31
38=31  false

There are no two consecutive even integers in which the smaller is added to three times the larger to get a result of 31.