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# During the first week of performances of a certain play

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Intern
Joined: 17 Jun 2011
Posts: 28
During the first week of performances of a certain play  [#permalink]

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07 Dec 2013, 07:56
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2
00:00

Difficulty:

(N/A)

Question Stats:

71% (02:15) correct 29% (01:54) wrong based on 84 sessions

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During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold was 25,200, how many of them were sold at full price?

A. 21,000
B. 19,800
C. 16,500
D. 15,800
E. 8,700
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Joined: 01 Sep 2010
Posts: 3416
Re: During the first week of performances of a certain play  [#permalink]

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07 Dec 2013, 09:07
1
5400 + x = 25200 then x is 19800

our x = 19800 is 6/5 of a certain number X

so 19800 = 6/5 of X ---> 19800 * 5 / 6 --> C is the answer
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Joined: 04 Jan 2015
Posts: 3158
Re: During the first week of performances of a certain play  [#permalink]

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04 May 2015, 06:38
Detailed Solution

Given:
The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.

Approach:
The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.

Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets sold i.e.

Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold

We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.

Working Out:
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold

Substituting values in the equation, we get
5,400 + 5x + x = 25,200
x= 3,300

Tickets sold at full price = 5x = 16,500

Regards
Harsh
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Re: During the first week of performances of a certain play  [#permalink]

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25 Nov 2019, 16:24
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Re: During the first week of performances of a certain play   [#permalink] 25 Nov 2019, 16:24
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