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# When it was found that 150 more tickets for the school play were sold

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Math Expert
Joined: 02 Sep 2009
Posts: 50711
When it was found that 150 more tickets for the school play were sold  [#permalink]

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17 Jul 2018, 23:31
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:35) correct 14% (02:29) wrong based on 28 sessions

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When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium. It was decided to have two performances. if the total number of tickets sold was equal to the total number who attended and if the auditorium was 2/3 full for each of the two performances, what is the seating capacity of the auditorium?

(A) 100
(B) 200
(C) 225
(D) 300
(E) 450

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Re: When it was found that 150 more tickets for the school play were sold  [#permalink]

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17 Jul 2018, 23:45
+1 for E.

Let,
N = Total Capacity of Auditorium

Therefore,
( 2/3 )*N + ( 2/3 )*N = 150 + N
N = 450

Hence, E.
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Re: When it was found that 150 more tickets for the school play were sold  [#permalink]

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18 Jul 2018, 01:15
Bunuel wrote:
When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium. It was decided to have two performances. if the total number of tickets sold was equal to the total number who attended and if the auditorium was 2/3 full for each of the two performances, what is the seating capacity of the auditorium?

(A) 100
(B) 200
(C) 225
(D) 300
(E) 450

Let the capacity of the auditorium be x.

Total tickets sold considering more than capacity = x+150

Now they decide to have 2 shows of equal no. of participants. So,

(x+150) /2

Now , we know that 2/3 of the capacity of the auditorium was full. We can form an equation :

(x+150) /2 = (2/3)x

x +150 = 4x / 3

3x +450 = 4x

x = 450. ( we assume x is the capacity )

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Re: When it was found that 150 more tickets for the school play were sold  [#permalink]

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22 Jul 2018, 17:14
Bunuel wrote:
When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium. It was decided to have two performances. if the total number of tickets sold was equal to the total number who attended and if the auditorium was 2/3 full for each of the two performances, what is the seating capacity of the auditorium?

(A) 100
(B) 200
(C) 225
(D) 300
(E) 450

We can let x = the seating capacity of the auditorium. So (x + 150) tickets were sold. There were 2 performances, each filling the auditorium at ⅔ capacity, so half of the total number of tickets sold is equal to 2/3 of the capacity of auditorium. Therefore, we have:

1/2(x + 150) = 2/3(x)

x/2 + 75 = 2x/3

Multiplying the equation by 6, we have:

3x + 450 = 4x

450 = x

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Re: When it was found that 150 more tickets for the school play were sold &nbs [#permalink] 22 Jul 2018, 17:14
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