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A theater charges $12 for seats in the orchestra and $8 for seats in

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A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 14 Sep 2015, 22:59
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Bunuel wrote:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.


Orchestra Seats - a
Balcony Seats - b

a+b = 350
and 12a + 8b = 3320

Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)

4a = 3320 - 8*350 = 3320 - 2800 = 520
i.e. a = 130
and b = 350-130 = 220

More seats in balcony than orchestra = b-a = 220 - 130 = 90

Answer: option A
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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 14 Sep 2015, 23:19
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1 statement gives us x+y=350
1 statement gives us 12x+8Y=3320
we can simplify 2nd statement as 3x+2y=830
mulitply 1st statement by 2 (2x+2x=700)
subtracting the two gives us
x=130
therefore y= 350-130=220
x-y= 90

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 15 Sep 2015, 01:25
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Bunuel wrote:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.


Orchestra tickets=x, Balcony tickets=350-x
(x*$12)+(350-x)*$8=$3320
12x+2800-8x=3320
4x=520
x=130
350-x=220
Difference in tickets=220-130=90
Answer A

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 15 Sep 2015, 01:40
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Bunuel wrote:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.


Solution: 12o + 8(350-o) = 3320 ==> 3o + 2(350-o) = 830 ==> o = 130 and b = 220
b - o = 220 - 130 = 90
Option A

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 15 Sep 2015, 06:20
No. of seats in Orchestra = x & No. of seats in Balcony = y
x+y = 350
12x+8y = 3320
Solving for x & y
x = 130, y = 220
No. of extra seats sold in the balcony = 220-130 = 90
Answer: A
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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 17 Sep 2015, 16:05
Bunuel wrote:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.


Let A be the number of seats in orchestra and B be the number of in balcony.
Then,
12A + 8B = 3320 .....(1)

A + B = 350 .....(2)

Solving equations (1) and (2)
We get A= 130 and B= 220
B-A = 90

Answer:- A

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 20 Sep 2015, 20:35
Bunuel wrote:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.


KAPLAN OFFICIAL SOLUTION:

The first step in this problem is to translate our word problem into math. We can write two equations based on the information in the question stem. If we call balcony seats B and orchestra seats R (we want to avoid using the letter O as a variable because it looks like the number 0), we can write one equation based on the number of seats sold and one equation based on the amount of money made. These equations are:

R + B = 350

12R + 8B = 3,320

Next, we need to combine these equations to solve for one of the variables. We can rewrite R + B = 350 as B = 350 – R and substitute (350 – B) in for R in our other equation. This gives us 12R + 8(350 – R) = 3,320. From here, we can solve for R as follows:

12R + 8(350 – R) = 3,320

12R + 2800 – 8R = 3,320

4R = 520

R = 130

Next we plug 130 in for R in our initial equation and solve for B:

130 + B = 350

B = 220

Finally, we need to find out how many more balcony seats than orchestra seats we have by subtracting the two results. This gives us 220 – 130 = 90, which is answer choice (A).
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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New post 18 Sep 2016, 22:44
Bunuel wrote:
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?

(A) 90
(B) 110
(C) 120
(D) 130
(E) 220


Kudos for a correct solution.

Can work through answers too
option*8<-(balcony) + 10<-(average 12 and 8) * (350-option) = total cost.
90*8 + 10(350-90) = 3320

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in [#permalink]

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Re: A theater charges $12 for seats in the orchestra and $8 for seats in   [#permalink] 04 Dec 2017, 19:51
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