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Age 14 to 16 Short Challenge Level:

When a speaker gave a talk, 6% of the audience slept through the whole thing.
22% of the audience stayed awake and heard the entire talk.

Of the rest of the audience, half of them heard $\frac{2}{3}$ of the talk, and half of them heard $\frac{1}{3}$ of the talk.

What was the average proportion of the talk that people heard?



This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.