produced the information:
285 watch football games
195 watch hockey games
115 watch basketball games
45 watch football and basketball
70 watch football and hockey
50 watch hockey and basketball
50 do not watch any of the three games
A. how many people in the survey watch all the three games?
B. How many people watch exactly one of the three games?
Let the number that watch the three games be x, then 50 - x watch hockey and basketball only 70 - x watch football and hockey only 45 - x watch football and basketball only 115 - (45 - x) - (50 - x) - x = 20 + x watch basketball only 195 - (70 - x) - (50 - x) - x = 75 + x watch hockey only 285 - (45 - x) - (70 - x) - x = 170 + x watch football only 50 do not watch any of the three games.
x + 50 - x + 70 - x + 45 - x + 20 + x + 75 + x + 170 + x + 50 = 500 480 + x = 500 x = 500 - 480 = 20
a.) therefore, 20 people watch all the three games.
b.) 20 + x + 75 + x + 170 + x = 265 + 3x = 265 + 3(20) = 265 + 60 = 325. Therefore, 325 people watch exaclty one of the three games.
