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31 Dec 2013, 07:21
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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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Re: For a recent play performance, the ticket prices were $25 pe [#permalink] ### Show Tags 31 Dec 2013, 07:22 3 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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: 16 Location: Uzbekistan Concentration: Finance, Entrepreneurship GMAT 1: 620 Q42 V33 GRE 1: 600 Q790 V400 GPA: 3.4 WE: Analyst (Commercial Banking) Followers: 0 Kudos [?]: 13 [1] , given: 57 Re: For a recent play performance, the ticket prices were$25 pe [#permalink]

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01 Jan 2014, 22:31
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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] ### Show Tags 02 Jan 2014, 00:57 1 This post received KUDOS 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 3872 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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05 Jan 2014, 11:54
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.

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Re: For a recent play performance, the ticket prices were $25 pe [#permalink] ### Show Tags 17 May 2016, 14:36 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: For a recent play performance, the ticket prices were$25 pe   [#permalink] 17 May 2016, 14:36
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