At a certain health club, 30% of the members use both pool a

well the wording is confusing (atleast to me )

giving it a try

P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
40% of (70-x) = x => 28 - 0.4x = x => x = 20% so only P = 70 -x = 50%

This problem belongs to overlapping sets not to percentage and interest.
by using tabular method with row : pool -- nopool and column: sauna | nosauna and by assuming total of members=100, one can easily solve this problem.

This question got me - I misunderstood the fact that 40% represents all people using the pool and the 30% represent the entire club members.

I'm trying to figure it out in another way to help me understand (although the overlapping sets method with the tables is probably the best)...

1. Let's assume that a total of 100 people use the pool.
2. From the question, 40% of them use the pool ONLY meaning 0.4 x 100 = 40 people. This means that 100-40=60 people uses the pool and sauna.
3. Also from the question, 30% of the ENTIRE CLUB uses the pool and sauna. If the 60 people from step 2 above uses the pool and sauna represents 30% of the entire club, that means there are 200 people in the club.
4. To find percentage of ALL people using the pool - 100/200 = 50%

Bunuel could you please help
i still find the question unclear
thank you

40 percent of the members who use the pool do not use the sauna, hence the remaining 60 percent of the members who use the pool use the sauna


BUT THOSE 60% must contain people who do not use the pool and only use sauna?

We can let the total number of members = 100 and x = the number of members who use the pool.

Thus, we have 30 members who use both the pool and sauna. Since 40 percent of the members who use the pool do not use the sauna, we know that 60 percent of the members who use the pool also use the sauna, and we already know that this number is 30. Thus, we can create the following equation:

0.6x = 30

x = 30/0.6 = 300/6 = 50

Thus, 50/100 = 50% of the members use the pool.

Answer: C

One way to look at this:
- 40 = pool
- 30 = pool + sauna
- 60 = sauna (100 minus 40)

so how many pool? Pool users total = pool + pool - (pool+sauna overlap) => 40 + (40 - 30) = 50%

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