GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 05 Dec 2019, 15:33

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The symphony sells two kinds of tickets: orchestra, for $40, and upper

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59561
The symphony sells two kinds of tickets: orchestra, for $40, and upper  [#permalink]

Show Tags

New post 07 May 2015, 03:41
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

93% (02:12) correct 7% (02:58) wrong based on 77 sessions

HideShow timer Statistics

The symphony sells two kinds of tickets: orchestra, for $40, and upper tiers, for $25. On a certain night, the symphony sells 90 tickets and gets $2625 in revenue from the sales. How many orchestra tickets did they sell?

A. 25
B. 35
C. 45
D. 55
E. 65


Kudos for a correct solution.
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 152
Re: The symphony sells two kinds of tickets: orchestra, for $40, and upper  [#permalink]

Show Tags

New post 07 May 2015, 07:01
1
Let o = number of orchestra tickets
Let u = number of upper tier tickets

We know that o + u = 90

-> o * 40 + u * 25 = 2.625

-> rephrase o + u = 90 to -> o = 90 - u and insert in the equation

(90 - u) * 40 + u * 25 = 2.625
3600 - 40u + 25u = 2.625
3600 - 15u = 2.625
-15u = - 975
u = 65


90 - 65 = number of orchestra tickets = 25
Intern
Intern
User avatar
Joined: 25 Nov 2014
Posts: 5
GMAT 1: 670 Q48 V34
The symphony sells two kinds of tickets: orchestra, for $40, and upper  [#permalink]

Show Tags

New post 07 May 2015, 07:04
1
Let orchestra tickets be: X
Therefore upper tiers tickets will be: 90-X

Now, the following equation can be made:
40X + 25(90-X) = 2625
40X + 2250 - 25X = 2625
15X = 375

Solving this, we get X = 25

Answer: A
Manager
Manager
User avatar
Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
The symphony sells two kinds of tickets: orchestra, for $40, and upper  [#permalink]

Show Tags

New post 07 May 2015, 10:01
1
Bunuel wrote:
The symphony sells two kinds of tickets: orchestra, for $40, and upper tiers, for $25. On a certain night, the symphony sells 90 tickets and gets $2625 in revenue from the sales. How many orchestra tickets did they sell?

A. 25
B. 35
C. 45
D. 55
E. 65


Kudos for a correct solution.



O + U = 90

45O * 25U = 2625

Two equations, two variables, solving will give O = 25

Hence, Answer is A
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59561
Re: The symphony sells two kinds of tickets: orchestra, for $40, and upper  [#permalink]

Show Tags

New post 11 May 2015, 04:06
Bunuel wrote:
The symphony sells two kinds of tickets: orchestra, for $40, and upper tiers, for $25. On a certain night, the symphony sells 90 tickets and gets $2625 in revenue from the sales. How many orchestra tickets did they sell?

A. 25
B. 35
C. 45
D. 55
E. 65


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Notice, in verbal form, this is a two-equations-two variables problem. The two variables are x = the number of orchestra tickets, and y = the number of upper tier tickets.

One equation we get is x + y = 90, for the total number of tickets sold. That’s one equation. If we sell x orchestra tickets, we get $40 for each, so we get 40x in total revenue from all of the orchestra tickets. Similarly, we get 25y in total revenue from all the upper tier tickets. Thus, the total revenue is 40x + 25y = 2625. That’s our second equation.

The first equation is incredibly convenient to multiply. I would rather multiply by 40 than by 25, so I make the coefficients of x match. I’ll multiply the first equation by 40, and the second equation by –1.

40x + 40y = 3600
(-40x - 25y = 2625)
_______________
15y = 975

Now, at first blush, that might look like an ugly division problem awaiting us, 975 divided by 15. Let’s break it down a bit. I know 900/3 = 300, and 75/3 = 25, so if I divide both sides by 3, I get

5y = 975/3 = 325

Now, 100/5 = 20, so three times that is 300/5 = 60. Of course, 25/5 = 5, so

y = 325/5 = 65

We want x, so x + (65) = 90 right x = 25, answer = A.

BTW, if these steps totally elude you, remember you can always backsolve from the numerical answers as a backup strategy.
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1870
Re: The symphony sells two kinds of tickets: orchestra, for $40, and upper  [#permalink]

Show Tags

New post 11 May 2015, 07:14
We are given that A + B = 90 (A and B representing both ticket types), and that 40A + 25B = 2625. You may factor out 5 from the latter equation just to make the numbers easier to work with. It becomes 8A + 5B = 525.
Since A + B = 90, then B= 90 - A. We are solving for A so it is easier to write the equation in terms of A.
8A + 5 (90-A) =525
8A + 450 - 5A= 525
3A=75
A=25
GMAT Club Bot
Re: The symphony sells two kinds of tickets: orchestra, for $40, and upper   [#permalink] 11 May 2015, 07:14
Display posts from previous: Sort by

The symphony sells two kinds of tickets: orchestra, for $40, and upper

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne