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 $\displaystyle x$ and $\displaystyle y$ as my numbers and this is what I got, based on the description:

$\displaystyle x$

$\displaystyle y=3x+4$

When multiplied, you get 407

$\displaystyle xy=407$

So, I substitute and simplify:

$\displaystyle x(3x+4)=407$

$\displaystyle 3x^2+4x=407$

$\displaystyle 3x^2+4x-407=0$

$\displaystyle (3x+37)(x-11)=0$

$\displaystyle x=-\frac{3}{37}, 11$

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

Now, substituting for $\displaystyle x=11$

$\displaystyle y=3x+4$

$\displaystyle y=3(11)+4$

$\displaystyle y=37$

and now I add:

$\displaystyle 37 + 11 = 48$

Thoughts?

Thanks in advance!