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Question Stats: 70% (01:33) correct 30% (01:41) wrong based on 700 sessions

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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.

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1

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 per adult an [#permalink] ### Show Tags 1 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 7644 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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GMAT 1: 590 Q45 V27 ### Show Tags

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) _________________ If you like this post, be kind and help me with Kudos! Cheers! VP  D Joined: 14 Feb 2017 Posts: 1281 Location: Australia Concentration: Technology, Strategy GMAT 1: 560 Q41 V26 GMAT 2: 550 Q43 V23 GMAT 3: 650 Q47 V33 GMAT 4: 650 Q44 V36 GMAT 5: 650 Q48 V31 GPA: 3 WE: Management Consulting (Consulting) Re: For a recent play performance, the ticket prices were$25 per adult an  [#permalink]

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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 _________________ Goal: Q49, V41 +1 Kudos if I have helped you GMAT Club Legend  V Joined: 12 Sep 2015 Posts: 4064 Location: Canada Re: For a recent play performance, the ticket prices were$25 per adult an  [#permalink]

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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 Answer: D Cheers, Brent _________________ Re: For a recent play performance, the ticket prices were$25 per adult an   [#permalink] 27 Apr 2019, 07:47
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