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boomtangboy
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A certain theater has 100 balcony seats. For every $2 increase in the 28 Apr 2012, 21:39
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A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


Show Spoiler
I solved it as follows:

10+2(x) = 100 -5(x)
x= 12
Why is my approach wrong?
ShowHide Answer
Official Answer
C
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Bunuel
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A certain theater has 100 balcony seats. For every $2 increase in the 29 Apr 2012, 04:51
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boomtangboy
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?
Show more

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

Answer: C.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

Answer: C.
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A certain theater has 100 balcony seats. For every $2 increase in the 12 May 2012, 05:16
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Bunuel
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A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

Answer: C.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

Answer: C.
Show more

@Bunuel,

in this chart, $17*80 = 1360.
why should we avoid 'D' as answer.?
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A certain theater has 100 balcony seats. For every $2 increase in the 12 May 2012, 11:56
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A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

Answer: C.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

Answer: C.

@Bunuel,

in this chart, $17*80 = 1360.
why should we avoid 'D' as answer.?
Show more

We can have ONLY one correct answer, so if C is correct then D is automatically wrong.

Also, we are told that "for every $2 increase in the price 5 fewer seats will be sold" and from $16 to $17 there is only $1 increase, so you cannot write $17*80.

Hope it's clear.
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A certain theater has 100 balcony seats. For every $2 increase in the 16 Oct 2014, 05:42
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A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

Answer: C.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

Answer: C.
Show more


Hey Bunuel,
What should we do with this piece of information?
If all the balcony seats are sold when the price of each seat is $10
shouldn't it be included in the total revenue from sale of tickets? something like
10y+(10+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$
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A certain theater has 100 balcony seats. For every $2 increase in the 16 Oct 2014, 07:51
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A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?

Equation should be (10+$2*x)(100-5x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,360 --> (5+x)(20-x)=136 --> x=3 or x=12 --> price=10+$2*3=$16 or price=10+$2*12=$34.

Answer: C.

But the easiest way to solve this problem would be to write down a chart:
$10*100=$1,000;
$12*95=$1,140;
$14*90=$1,260;
$16*85=$1,360.

Or do the other way around and plug the answer choices.

Answer: C.


Hey Bunuel,
What should we do with this piece of information?
If all the balcony seats are sold when the price of each seat is $10
shouldn't it be included in the total revenue from sale of tickets? something like
10y+(10+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$
Show more

No. The number of tickets sold at $10 is 100. We are told that the theater has 100 balcony seats and all the balcony seats are sold when the price of each seat is $10. Check the red portion of my solution above.
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A certain theater has 100 balcony seats. For every $2 increase in the 17 Feb 2021, 17:35
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boomtangboy
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


Show more

Solution:

Let’s let x = the number of two-dollar increases in the ticket price above $10. So (10 + 2x) = the (increased) price of the ticket, and (100 - 5x) = the number of tickets sold at that increased ticket price. We know that (ticket price) x (no. of tickets sold) = total revenue, so we have the following equation:

(10 + 2x)(100 - 5x) = 1360

1000 + 200x - 50x - 10x^2 = 1360

-1000 - 150x +10x^2 = -1360

10x^2 - 150x + 360 = 0

x^2 - 15x + 36 = 0

(x - 3)(x - 12) = 0

x = 3 or x = 12

If x = 3, then the price of a balcony seat is 10 + 2(3) = $16. If x = 12, then the price of a balcony seat is 10 + 2(12) = $34. Since only $16 is given in the answer choices, it’s the correct answer.

Alternate Solution:

Let’s test the answer choices.

A) 1,360 is not divisible by 3; therefore, it is not divisible by 12. Since the price of a balcony seat must be a factor of 1,360, it cannot be $12.

B) 1,360 is not divisible by 7; therefore, it is not divisible by 14. Since the price of a balcony seat must be a factor of 1,360, it cannot be $14.

C) Notice that 1,360/16 = 85. We see that there are three increases in the amount of $2 from $10 to $16; therefore, the number of tickets sold must be 3 x 5 = 15 less than the total number of balcony seats. Since 85 is indeed 15 less than 100, this is a possible value for the price of a balcony seat.

Answer: C
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A certain theater has 100 balcony seats. For every $2 increase in the 04 Jul 2022, 15:58
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A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


I solved it as follows:

10+2(x) = 100 -5(x)
x= 12

Why is my approach wrong?
Show more

The algebra isn't bad on this one, but since I love Pluggin In The Answers (PITA) so much,...

I like trying B and D.

B: $14*90 tickets = $1260. Not enough.

D: $17*85 tickets = $1445. Too much.

We need something in the middle.

Answer choice C.


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A certain theater has 100 balcony seats. For every $2 increase in the 09 Aug 2023, 21:44
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boomtangboy
A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?

A. $12
B. $14
C. $16
D. $17
E. $18


Show Spoiler
I solved it as follows:

10+2(x) = 100 -5(x)
x= 12
Why is my approach wrong?
Show more

Hi,
I solved it this way.
What you have to recognise is that the revenue is the product of number of seats and value of the ticket.

I took the LCM of 1360.
I kept factoring out 2 till I reached 2^4*85

So the ticket value of the ticket is 16 and 85 is the number of seats.
Option C
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A certain theater has 100 balcony seats. For every $2 increase in the 28 Jun 2024, 07:03
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A long shot but check if the result - $1,360 is divisible by the answers. Only C and D fit. The price change is $2 per ticket hence the result must be even. Only C fits.
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A certain theater has 100 balcony seats. For every $2 increase in the 28 Jul 2025, 02:36
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