For a recent play performance, the ticket prices were $25 per adult an

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.
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The best answer is D!

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.

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



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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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)

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

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

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
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