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# For a recent play performance, the ticket prices were $25 pe  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Math Expert Joined: 02 Sep 2009 Posts: 17307 Followers: 2873 Kudos [?]: 18374 [0], given: 2348 For a recent play performance, the ticket prices were$25 pe [#permalink]  31 Dec 2013, 06:21
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Difficulty:

35% (medium)

Question Stats:

58% (02:12) correct 41% (01:31) wrong based on 46 sessions
The Official Guide For GMAT® Quantitative Review, 2ND Edition

For a recent play performance, the ticket prices were $25 per adult and$15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults?

(1) Revenue from ticket sales for this performance totaled $10,500. (2) The average (arithmetic mean) price per ticket sold was$21.

Data Sufficiency
Question: 14
Category: Algebra Simultaneous equations
Page: 154
Difficulty: 650

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Math Expert
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Re: For a recent play performance, the ticket prices were $25 pe [#permalink] 31 Dec 2013, 06:22 Expert's post SOLUTION For a recent play performance, the ticket prices were$25 per adult and $15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults? (1) Revenue from ticket sales for this performance totaled$10,500 --> 25a+15c=10,500 --> 25a+15(500-a)=10,500. We can solve for a. Sufficient.

(2) The average (arithmetic mean) price per ticket sold was $21 --> \frac{25a+15c}{500}=21 --> 25a+15c=10,500. The same info as above. Sufficient. Answer: D. _________________ Intern Joined: 03 Dec 2013 Posts: 18 Location: United States Concentration: Finance, Entrepreneurship GMAT Date: 05-21-2014 GRE 1: 600 Q790 V400 GPA: 3.4 WE: Analyst (Commercial Banking) Followers: 0 Kudos [?]: 10 [1] , given: 28 Re: For a recent play performance, the ticket prices were$25 pe [#permalink]  01 Jan 2014, 21:31
1
KUDOS

After reading the given problem we get this problem:
x +y = 500
25x +15y = (The sum of money spent for tickets)=> This is what we need to solve the problem.

(1) is sufficient. It tells us about revenue which is the sum of all prices of tickets.
(2) is also sufficient. If we have average price and the number of all tickets then we can find the total sum.
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Re: For a recent play performance, the ticket prices were $25 pe [#permalink] 01 Jan 2014, 23:57 For a recent play performance, the ticket prices were$25 per adult and $15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults? (1) Revenue from ticket sales for this performance totaled$10,500.
(2) The average (arithmetic mean) price per ticket sold was $21. Sol: Let A = Total no. of Adult tickets C: Total no. of Child Tickets Given A+C=500, we need to find A ? Price of Adult Ticket:$25
Price of Child Ticket : $15 From St 1, we have 25*A+15*C = 10500 We also know A+C= 500 We have 2 variables and 2 equations and therefore we can solve for A. We can leave it that. So B C and E ruled out From St 2 we have Average price is$ 21. Refer attachment

Attachment:

WA.PNG [ 12.23 KiB | Viewed 410 times ]

Now $21 is 6$ more than Child Ticket price and $4 Less than Adult ticket price. So by Weighted Average principle. Total difference between Adult and Child Ticket price is$ 10

Number of Adult Tickets will be: 6/10 *500 = 300 -----> A

Just for clarity purpose we can calculate St 1 as well

5A+3C= 2100-------Eq 1
A+C=500-----> 3A+3C= 1500-------> Eq 2

Subtracting 2 from1, we get 2A=600 or A =300.

Ans D
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Re: For a recent play performance, the ticket prices were $25 pe [#permalink] 02 Jan 2014, 00:17 Since the question asks for the number of tickets sold for adults, let us assume x to be the number of tickets sold to adults. Average price/ticket = (no. of adult tickets) * (Price/adult ticket) + (no. of child tickets) * (Price/child ticket) Av. price = 25 * A + 15 * C Since A + C = 500; C = 500 - A Av. price = 25A + 15(500 - A) = 25A + 7500 - 15A = 10A + 7500; So, if we know the av.price/ticket, we can A; 1) Av.price = 10500/500 = 21; Sufficient 2) Av.price is given as 21; Sufficient. Hence (D). Math Expert Joined: 02 Sep 2009 Posts: 17307 Followers: 2873 Kudos [?]: 18374 [0], given: 2348 Re: For a recent play performance, the ticket prices were$25 pe [#permalink]  05 Jan 2014, 10:54
Expert's post
SOLUTION

For a recent play performance, the ticket prices were $25 per adult and$15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults?

(1) Revenue from ticket sales for this performance totaled $10,500 --> 25a+15c=$10,500 --> 25a+15(500-a)=$10,500. We can solve for a. Sufficient. (2) The average (arithmetic mean) price per ticket sold was$21 --> \frac{25a+15c}{500}=21 --> 25a+15c=$10,500. The same info as above. Sufficient. Answer: D. _________________ Re: For a recent play performance, the ticket prices were$25 pe   [#permalink] 05 Jan 2014, 10:54
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