When a survey of 800 people was done, 55 percent of those surveyed said they ate candy, 65 percent said they ate chips, and 90 percent said they ate hotdogs. What is the smallest possible number of people who said they ate candy, chips and hotdogs.

Source: MathMovesU MATH CHALLENGE PROBLEM - 2012/04/19

Level: Junior

Among the 800 surveryed people, 1- 55% = 45% of them said they did not eat candy, 1-65% = 35% said they did not eat chips, and 1-90% = 10% said they did not eat hotdogs. Thus at most 45%+35%+10% = 90% said they did not eat candy, did not eat chips, or did not eat hotdogs. It follows that smallest possible number of people who said they ate candy, chips and hotdogs is (1-90%)*800 = 80.