Takeaway Time

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



$35$ teenagers were asked what takeaways they liked to eat.

 

$24$ answered Chinese
$16$ answered Indian
$10$ answered pizza


None of the teenagers liked all three.

All who liked pizza also liked Chinese.

$9$ of the Chinese fans didn't like either Indian or pizza.

 

If all the teenagers liked at least one, how many liked only Indian?