Solving a word problem using a Venn diagram 
problem: In a group of $265$ persons, $200$ like singing, $110$ like dancing and $55$ like painting.
If $60$ persons like both singing and dancing, $30$ like both singing and painting and $10$ like all the activities, then how many like only dancing and painting?

Solution:

Also $x+y =50$ and $y+z=25$.
I want to find $y+10$.

You have three unknowns ($x, y, z$) and knowing the total number of people gives you the third equation that you need to solve the system. In other words, you have:
$$
\begin{align}
y+x=50\\
y+z=25\\
y+x+z=65
\end{align}
$$
which hopefully should not be a problem to solve.
