Question 73918
Let's make the first number equal to "x." Then, since it's consecutive, the other two numbers are {{{(x+1)}}} and {{{(x+2)}}}.

With this we can make an equation: (using the other information provided)
{{{2(x+(x+1))=3(x+2)+10}}}
From this, we get {{{x=14}}}
So, the numbers are 14, 15, and 16.