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Bunuel
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


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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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Bunuel
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


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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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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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Bunuel
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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Bunuel
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


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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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Bunuel
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


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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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Bunuel
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.
\(­12o + 8b = 3320 \)----------->(I)
\(o + b = 350\)----------->(II)

(II)*12 = \(12o + 12b = 4200\)----------->(III)

(III) - (I) => \(4b = 880\)

Thus, \(b = 220\) substituting the value in (II) we get \(o = 130\)

So, \(b - o = 220 - 130 = 90\), Answer must be (A)
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