A survey was conducted among 40 tourists. The results were
28 visited Antigua (A)
30 visited Barbados (B)
3x visited both A and B
x visited neither
(i) Write an expression in x to represent the TOTAL number of tourists in the survey.
(ii) Calculate the value of x.
Please explain. I really can't understand how to answer the questions. It seems like it is an impossible answer.
28 visited Antigua (A)
30 visited Barbados (B)
3x visited both A and B
x visited neither
(i) Write an expression in x to represent the TOTAL number of tourists in the survey.
(ii) Calculate the value of x.
Please explain. I really can't understand how to answer the questions. It seems like it is an impossible answer.
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Ugh. I'll take a stab at it, though I'm working on a poor memory for this stuff, and maybe a better mathematician will weigh in.
Draw two intersecting circles representing your sets and the overlap. Circle A contains 58 items (tourists who visited Antigua),circle B contains 30 items (Barbados tourists) and the overlap between them is 3x - as defined by the problem. Draw another independent circle that contains X tourists- those that visited neither Barbados nor Antigua.
Now you can set up the algebraic relationship. Remember that you have 40 tourists total. That overlap between sets A and B- equal to 3X- can be subtracted from the sum of the two sets (58 plus 30) and the independent set (x) to equal the total: 40. So:
28 + 30 - 3x + x = 40
58 - 2x = 40
-2x = -18
x = 9
It looks like only one tourist went to Antigua exclusively, 27 went to both islands, and only 3 went to Barbados alone. 9 folks evidently went somewhere else. It would help if I could sketch the diagram here, but I hope you get the idea.
Draw two intersecting circles representing your sets and the overlap. Circle A contains 58 items (tourists who visited Antigua),circle B contains 30 items (Barbados tourists) and the overlap between them is 3x - as defined by the problem. Draw another independent circle that contains X tourists- those that visited neither Barbados nor Antigua.
Now you can set up the algebraic relationship. Remember that you have 40 tourists total. That overlap between sets A and B- equal to 3X- can be subtracted from the sum of the two sets (58 plus 30) and the independent set (x) to equal the total: 40. So:
28 + 30 - 3x + x = 40
58 - 2x = 40
-2x = -18
x = 9
It looks like only one tourist went to Antigua exclusively, 27 went to both islands, and only 3 went to Barbados alone. 9 folks evidently went somewhere else. It would help if I could sketch the diagram here, but I hope you get the idea.