Question 1191783: Of the 65 adults in a group, 40 enjoy reading and 21 enjoy going to movies. The number of
adults who do not enjoy either activities is twice the number of adults who enjoy both activities.
a. By taking x to be the number of adults who enjoy both reading and movies, draw a Venn
diagram to illustrate the information.
b.Hence, find the number of adults who
i. Enjoy only either reading or movies
ii. Enjoy neither reading nor movies.
Answer by ikleyn(52805)   (Show Source):
You can put this solution on YOUR website! .
Of the 65 adults in a group, 40 enjoy reading and 21 enjoy going to movies. The number of
adults who do not enjoy either activities is twice the number of adults who enjoy both activities.
a. By taking x to be the number of adults who enjoy both reading and movies, draw a Venn
diagram to illustrate the information.
b.Hence, find the number of adults who
i. Enjoy only either reading or movies
ii. Enjoy neither reading nor movies.
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Let x be the number of those adults who enjoy both activities.
Then the number of those who do not enjoy either activities is 2x, according to the problem.
As you read the problem, you can write this equation
65 = 2x + (40 + 21 -x). (1)
Notice that the value in parentheses is the number of those adults who enjoy at least one of the two activities.
From equation (1), you have
65 - 40 - 21 = 2x - x
4 = x.
Thus the number of those who enjoy both activities is 4;
The number of those who enjoy neither reading nor movies is 2*4 = 8. It is the ANSWER to question ii.
The number of those who enjoy only either reading or movies is (40-4) + (21-4) = 53. It is the ANSWER to question i.
Solved.
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