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In a recreation club with 212 members, 130 participate in kickboxing a
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14 Jun 2023, 16:48
14 Jun 2023, 16:48
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90% (02:03) correct
9% (02:45) wrong based on 22 sessions
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In a recreation club with 212 members, 130 participate in kickboxing and 110 participate in rowing. If at least 10 % of the club's members participate in neither kickboxing nor rowing, what's the minimum number of members who participate in both
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50
Re: In a recreation club with 212 members, 130 participate in kickboxing a
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15 Jun 2023, 04:19
15 Jun 2023, 04:19
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212 = 130 + 110 - Both + None
Both = None + 28
None = atleast 10% of 212 = 22(closest integer greater than 21.2)
Both = 50
Both = None + 28
None = atleast 10% of 212 = 22(closest integer greater than 21.2)
Both = 50
Re: In a recreation club with 212 members, 130 participate in kickboxing a
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17 Jun 2023, 04:00
17 Jun 2023, 04:00
Expert Reply
OE
At least 10 % of the recreation club participates in neither kickboxing nor rowing. Therefore, at least 10% ( 212) = 21.2 people are in neither activity. Since only integer numbers of members can exist, at least 22 members must not participate in either activity.
For the “Neither” category to reach \(\geq 22\), the kickboxing and rowing circles have to include no more than 212 - >22 = <100 members. Thus, since there are 130 + 110 = 240 "memberships” in the kickboxing and rowing activities combined, there has to be an "overlap” of at least 50 members in both activities.
Thus, in the scenario where exactly 30 members are involved in both kickboxing and rowing, there are 80 members involved in kickboxing only, 60 involved in rowing only, and 22 involved in neither. Thus, 50 + 80 + 60 + 22 sums to 212, so the goal has been achieved.
At least 10 % of the recreation club participates in neither kickboxing nor rowing. Therefore, at least 10% ( 212) = 21.2 people are in neither activity. Since only integer numbers of members can exist, at least 22 members must not participate in either activity.
For the “Neither” category to reach \(\geq 22\), the kickboxing and rowing circles have to include no more than 212 - >22 = <100 members. Thus, since there are 130 + 110 = 240 "memberships” in the kickboxing and rowing activities combined, there has to be an "overlap” of at least 50 members in both activities.
Thus, in the scenario where exactly 30 members are involved in both kickboxing and rowing, there are 80 members involved in kickboxing only, 60 involved in rowing only, and 22 involved in neither. Thus, 50 + 80 + 60 + 22 sums to 212, so the goal has been achieved.
