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# For a recent play performance, the ticket prices were $25 per adult an SORT BY: Tags: Show Tags Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 94609 Own Kudos [?]: 643688 [37] Given Kudos: 86737 Most Helpful Reply Math Expert Joined: 02 Sep 2009 Posts: 94609 Own Kudos [?]: 643688 [14] Given Kudos: 86737 General Discussion Intern Joined: 03 Dec 2013 Posts: 6 Own Kudos [?]: 29 [2] Given Kudos: 57 Location: Uzbekistan Concentration: Finance, Entrepreneurship GMAT 1: 620 Q42 V33 GRE 1: Q790 V400 GPA: 3.4 WE:Analyst (Commercial Banking) Director Joined: 25 Apr 2012 Posts: 529 Own Kudos [?]: 2322 [2] Given Kudos: 740 Location: India GPA: 3.21 WE:Business Development (Other) Re: For a recent play performance, the ticket prices were$25 per adult an [#permalink]
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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 $21. Refer attachment Attachment: WA.PNG [ 12.23 KiB | Viewed 20502 times ] Now$ 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 Manager Joined: 21 Mar 2011 Status:GMATting Posts: 96 Own Kudos [?]: 288 [1] Given Kudos: 104 Concentration: Strategy, Technology GMAT 1: 590 Q45 V27 Re: For a recent play performance, the ticket prices were$25 per adult an [#permalink]
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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).
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Re: For a recent play performance, the ticket prices were $25 per adult an [#permalink] nutshell wrote: 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). This is more clean D x: the tickets sold were for adults 1) 25x + (500-x)*15 = 10500 => sufficient 2) The average (arithmetic mean) price per ticket sold was$21.
=> Revenue from ticket sales 500x21 = 10500
=> sufficient because it' has the same condition with 1)
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Re: For a recent play performance, the ticket prices were $25 per adult an [#permalink] 1 Bookmarks Got this wrong in a GMATFocus test, but I realise I just made silly mistakes. 25A + 15C = Total$ However, we are told the # tickets sold, so lets include this now
25A + 15(500-A) = Total$1. Total$ = 10,500
25A + 15(500-A) = 10,500.

Sufficient to solve for A

2. [25A + 15(500-A)]/500 = 21
25A + 15(500-A) = 21*500
25A + 15(500-A) = 10,500 (Sufficient to solve for A

D
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Re: For a recent play performance, the ticket prices were $25 per adult an [#permalink] Expert Reply Top Contributor Bunuel wrote: 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. Target question: How many of the tickets sold were for adults? Given: A total of 500 tickets were sold for the performance Let C = # of child tickets sold Let A = # of adult tickets sold So, C + A = 500 Statement 1: Revenue from ticket sales for this performance totaled$10,500
In other words, 25A + 15C = 10,500
When we add our given equation, C + A = 500, we can see that we have a system of 2 different linear equations with 2 variables.
Since we COULD solve this system for A, we COULD answer the target question with certainty.
So statement 1 is SUFFICIENT

Statement 2: The average (arithmetic mean) price per ticket sold was $21. We'll use this fact: average of n numbers = (sum of the n numbers)/n Rearrange to get sum of the n numbers = (average of n numbers)(n) If 500 tickets were sold and the average ticket price was$21, then the sum of all tickets sold = (21)(500) = $10,500 IMPORTANT: Statement 2 is just another way of telling us that the total revenue from ticket sales was$10,500 (this is exactly what statement 1 told us)
Since statement 1 was SUFFICIENT, statement 2 must also be SUFFICIENT

Cheers,
Brent
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Re: For a recent play performance, the ticket prices were $25 per adult an [#permalink] 1 Kudos Expert Reply Bunuel wrote: 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. Solution: Question Stem Analysis: We need to determine the number of adult tickets sold in a recent play performance, given that an adult ticket is$25 and a child ticket is $15. If we let x = the number of adult tickets sold and y = the number of child tickets sold, we can create the equation x + y = 500 for the total number of tickets sold. We need to determine the value of x. Statement One Alone: Since the total revenue raised from the ticket sales was$10,500, we can create another equation: 25x + 15y = 10,500. Along with the equation x + y = 500, we see that we can solve for the value of x (and y). Statement one alone is sufficient.

Statement Two Alone:

Since the average price per ticket sold is $21, we can create another question (25x + 15y) / 500 = 21. Along with the equation x + y = 500, we see that we can solve for the value of x (and y). Statement two alone is sufficient. Answer: D Non-Human User Joined: 09 Sep 2013 Posts: 34083 Own Kudos [?]: 853 [0] Given Kudos: 0 Re: For a recent play performance, the ticket prices were$25 per adult an [#permalink]
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Re: For a recent play performance, the ticket prices were \$25 per adult an [#permalink]
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