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** : ![Venn diagram]( 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.