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Math Expert V
Joined: 02 Sep 2009
Posts: 59658
The symphony sells two kinds of tickets: orchestra, for \$40, and upper  [#permalink]

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Difficulty:   15% (low)

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

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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.

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Manager  Joined: 07 Apr 2015
Posts: 152
Re: The symphony sells two kinds of tickets: orchestra, for \$40, and upper  [#permalink]

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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  Joined: 25 Nov 2014
Posts: 5
GMAT 1: 670 Q48 V34 The symphony sells two kinds of tickets: orchestra, for \$40, and upper  [#permalink]

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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

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

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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

Math Expert V
Joined: 02 Sep 2009
Posts: 59658
Re: The symphony sells two kinds of tickets: orchestra, for \$40, and upper  [#permalink]

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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.
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Joined: 06 Nov 2014
Posts: 1870
Re: The symphony sells two kinds of tickets: orchestra, for \$40, and upper  [#permalink]

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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 Re: The symphony sells two kinds of tickets: orchestra, for \$40, and upper   [#permalink] 11 May 2015, 07:14
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