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

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At a certain health club, 30% of the members use both the [#permalink]  22 Jul 2006, 10:16
At a certain health club, 30% of the members use both the pool and sauna, but 40% of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

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Re: percentage problem [#permalink]  22 Jul 2006, 11:06
cejismundo wrote:
At a certain health club, 30% of the members use both the pool and sauna, but 40% of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

Let total = T, use pool = P, use sauna = S
P&S : 0.3T
40% of the members who use the pool do not use the sauna means that "60% of the members who use pool use the sauna."
0.6P = 0.3T
P = 1/2T

thus, 50% use the pool
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Re: percentage problem [#permalink]  22 Jul 2006, 16:17
cejismundo wrote:
At a certain health club, 30% of the members use both the pool and sauna, but 40% of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

Damn, took me too long to solve this, I am so out of practice.

The problem is actually pretty simple.

Let total number of members be X, set of members using the pool be P, and set of members using the sauna be S.

Then PS = 0.3X
PS=0.6P
P=PS/0.6=0.3X/0.6=X/2

Therefore 1/2 the members use the pool, as a percentage its 50%
Re: percentage problem   [#permalink] 22 Jul 2006, 16:17
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