57 people can speak English only.

How to see this

Let:

  • EEE: people who speak English, ∣E∣=72|E|=72∣E∣=72.
  • FFF: people who speak French, ∣F∣=43|F|=43∣F∣=43.
  • Total people ∣E∪F∣=100|E\cup F|=100∣E∪F∣=100 (everyone speaks at least one language).

Use the inclusion–exclusion principle for two sets:

∣E∩F∣=∣E∣+∣F∣−∣E∪F∣|E\cap F|=|E|+|F|-|E\cup F|∣E∩F∣=∣E∣+∣F∣−∣E∪F∣

∣E∩F∣=72+43−100=15|E\cap F|=72+43-100=15∣E∩F∣=72+43−100=15

So 15 people speak both English and French.

Those who speak English only are:

∣E∣−∣E∩F∣=72−15=57|E|-|E\cap F|=72-15=57∣E∣−∣E∩F∣=72−15=57

Therefore, the number of people who can speak English only is 57.