The Venn diagram below shows the number of people in a youth club (U) who play music (M) and sport (S), where n ∈ N - Junior Cycle Mathematics - Question 8 - 2019
Question 8
The Venn diagram below shows the number of people in a youth club (U) who play music (M) and sport (S), where n ∈ N.
The Venn diagram shows:
- 52 people play only m... show full transcript
Worked Solution & Example Answer:The Venn diagram below shows the number of people in a youth club (U) who play music (M) and sport (S), where n ∈ N - Junior Cycle Mathematics - Question 8 - 2019
Step 1
Make n as big as possible
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Answer
To find the maximum number of people who could be in the youth club, we first need to express the total number of people in terms of n. The formula for the total number of people in the youth club is:
52+(184−n)+125+2n
This simplifies to:
361+n.
Step 2
Max number of people
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Answer
Given that M∩S=184−n, the maximum value of n can be found when:
M∩S=184−n=0
From this, we find that the maximum number of people is:
361+n=361+184=545.
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