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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

Ahow many people in the survey watch all the three games?

BHow many people watch exactly one of the three games?

Verified Answer :

nobillionaireNobley

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.