Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of $10$ hours per week helping around the house for $6$ weeks. For the first $5$ weeks she helps around the house for $8$, $11$, $7$, $12$ and $10$ hours. How many hours must she work for the final week to earn the tickets?
$\mathrm{(A)}\ 9 \qquad\mathrm{(B)}\ 10 \qquad\mathrm{(C)}\ 11 \qquad\mathrm{(D)}\ 12 \qquad\mathrm{(E)}\ 13$
Let $x$ be the number of hours she must work for the final week. We are looking for the average, so  
\[\frac{8 + 11 + 7 + 12 + 10 + x}{6} = 10\]  
Solving gives:
\[\frac{48 + x}{6} = 10\]
\[48 + x = 60\]
\[x = 12\]
So, the answer is $\boxed{\textbf{(D)}\ 12}$