a survey of 500 television watchers

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.