Hey, everyone!

I'm having a little trouble with this one... I'm pretty sure I'm missing something, though. Here's the problem:

"The product of two numbers is 407. One of the numbers is three times the other number, augmented by four. Find the sum of the two numbers."

So, I chose and as my numbers and this is what I got, based on the description:

When multiplied, you get 407

So, I substitute and simplify:

I'm assuming the solution I should choose is the 11, right?

Now, substituting for

and now I add:

Thoughts?

Thanks in advance!