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# At a play , 5% of the patrons are late and seated immediatel

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Director
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At a play , 5% of the patrons are late and seated immediatel [#permalink]

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16 Aug 2010, 08:25
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At a play, 5% of the patrons are late and seated immediately, but 30% of the patrons who are lateare not seated until the end of Act 1. approx what percent of the patrons are late
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16 Aug 2010, 08:58
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rxs0005 wrote:
At a play , 5% of the patrons are late and seated immediately , but 30% of the patrons who are late are not seated until the end of Act 1. approx what percent of the patrons are late

Interesting question. Let me try to solve this.

Suppose total number of patrons is 100.

Let x be the number of patrons who are late.

Then, as per the statement,

Quote:
5% of the patrons are late and seated immediately

Patrons who are late but allowed to seat = 5

and

Quote:
30% of the patrons who are late are not seated until the end of Act 1.

Patrons who are late but are not allowed to seat = 0.3x

Now we know, Total number of patrons who are late = Number of patrons who are late but allowed to seat + Number of patrons who are late but are not allowed to seat
=> x = 5 + 0.3x
=> 0.7x = 5
=> x = 5/0.7 = 50/7

So, percentage of patrons who are late = 50/7% ~ 7.1%

Hope this will help.
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16 Aug 2010, 09:04
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Total patrons X
Late patrons L
Seated imm = 0.05X
Seated after Act1 = 0.3L
So 0.05X+0.3L=L

L/X = 5/0.7
= 7%

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20 Aug 2010, 15:10
I agree, 7%.

Hey mainhoon, what kind of mobile you have?, is it comfortable for you to write in this forum?
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03 Dec 2012, 02:43
I found this chart from MGMAT really helpful. The two columns represent those who are Late and not Late. The to rows represent those who are seated immediately and not seated immediately. We use the concrete number 100 to denote the patrons.

5 will be placed in the cell of those late and seated immediately.
X to represent the total of late patrons both seated immediately and not.
It is given that 30 percent of those late are not seated. Thus, we know 70 percent of those late are.

.7x = 5
X = 5/.7 = 50/7 ~ 7.14

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Re: Word problem   [#permalink] 03 Dec 2012, 02:43
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