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# A certain theater has 100 balcony seats. For every \$2

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Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
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A certain theater has 100 balcony seats. For every \$2  [#permalink]

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28 Apr 2012, 21:39
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Difficulty:

65% (hard)

Question Stats:

65% (02:42) correct 35% (02:48) wrong based on 724 sessions

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 59628
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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29 Apr 2012, 04:51
5
7
boomtangboy wrote:
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.

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.

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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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30 Apr 2012, 03:53
1
Here's a long winded approach!

Think about a supply and demand chart, but put price along the x axis.

We are told:
Q = mP + C
(10,100)
(12,95)

Which is enough to work out the equation:

Work out m, m = (100-95) / (10 - 12) = -5 / 2
Solve for C

Hence Q = -5/2P + 125

Great. So for any given P, we now know Q seats were sold, but we are interested in total revenue

TR = Q * P = 1360, so

Q*P = -5/2P^2 + 125P
1360 = -5/2P^2 + 125P
2720 = -5P^2 + 250P
5P^2 - 250P + 2720 = 0
P^2 - 50P + 544 = 0

(P - 16)(P - 34) = 0
P = 16, P = 34

16.
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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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01 May 2012, 07:54
The official answer given here is wrong, it is given E. Moderators please correct it, it'll be C.
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Joined: 02 Jun 2011
Posts: 112
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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12 May 2012, 05:16
Bunuel wrote:
boomtangboy wrote:
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.

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.

@Bunuel,

in this chart, \$17*80 = 1360.
why should we avoid 'D' as answer.?
Math Expert
Joined: 02 Sep 2009
Posts: 59628
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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12 May 2012, 11:56
kashishh wrote:
Bunuel wrote:
boomtangboy wrote:
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.

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.

@Bunuel,

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

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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Posts: 59628
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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31 May 2013, 06:22
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Posts: 5
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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02 Jun 2013, 21:49
Hello Bunuel,
I solved it the following way. Let me know if I am correct in the logic and the approach.

R1 = 1000; revenue when price per seat = \$10 and no. of seats are 100
R2 = 1360; revenue when price increase every time by \$2 and 5 lesser no of seats sold that every time.

Hence, for R2,
x = no. of times price of each seat increase by \$2
n = no. of times 5 lesser seats are sold when each time the price is increased by \$2

Incremental revenue = \$ 360

Now,
essentially x = n (since everytime the price is increased, lesser no. of seats are sold) and this is attributed to the incremental revenue

the number of times the price is increased by \$2 = 2x
the number of times 5 lesser seats are sold = 5n

hence,
2x * 5n = 360
10xn = 360
xn = 36

now, as mentioned above, x = n
hence x^2= 36
giving, x = + / - 6

x cannot be -6 since the price is increased, thus making x = 6

hence the new price during R2 (1360) = 10+6 = \$16

thanks,
Rohan
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Posts: 5
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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02 Jun 2013, 21:56
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

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.

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.

Hello Bunuel,
I solved it the following way. Let me know if I am correct in the logic and the approach.

R1 = 1000; revenue when price per seat = \$10 and no. of seats are 100
R2 = 1360; revenue when price increase every time by \$2 and 5 lesser no of seats sold that every time.

Hence, for R2,
x = no. of times price of each seat increase by \$2
n = no. of times 5 lesser seats are sold when each time the price is increased by \$2

Incremental revenue = \$ 360

Now,
essentially x = n (since everytime the price is increased, lesser no. of seats are sold) and this is attributed to the incremental revenue

the number of times the price is increased by \$2 = 2x
the number of times 5 lesser seats are sold = 5n

hence,
2x * 5n = 360
10xn = 360
xn = 36

now, as mentioned above, x = n
hence x^2= 36
giving, x = + / - 6

x cannot be -6 since the price is increased, thus making x = 6

hence the new price during R2 (1360) = 10+6 = \$16

thanks,
Rohan
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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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06 Jul 2014, 21:46
(final price)*(final seats sold) = 1360

so either (final price) or (final seats sold) should be a factor of 1360

A. 1360/12 indivisible
B. 1360/14 indivisible
C. 1360/16 = 85 (final seats sold) divisible, correct
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Posts: 32
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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16 Oct 2014, 05:42
Bunuel wrote:
boomtangboy wrote:
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.

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.

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\$
Math Expert
Joined: 02 Sep 2009
Posts: 59628
Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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16 Oct 2014, 07:51
1
saggii27 wrote:
Bunuel wrote:
boomtangboy wrote:
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.

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.

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\$

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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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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16 Oct 2014, 10:46
Bunuel wrote:
saggii27 wrote:
Bunuel wrote:
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.

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.

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\$

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.[/quote]

got it thanks.

kudos!!!
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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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16 Oct 2014, 23:15
boomtangboy wrote:
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

This seems to be another brilliant question, which seems easy, but has a small trap. If we start from option E, we would realize that even 17 divides 1360. But, that can not be the correct choice, since the increase in price d be \$2
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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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09 Dec 2015, 20:14
solved it as everyone else:
1360=1000+150x-10x^2
or (x-3)(x-12)

now, either x is 3 or 12. if 12, then the price would be 12*2+10 => 34\$. Since we don't have it in our answer choices, it must be the other case, when x is 3.

if x is 3, then the price is 3*2+10 = 16.
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A certain theater has 100 balcony seats. For every \$2  [#permalink]

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20 Jan 2016, 15:37
let 10+x=seat price
100-2.5x=number of seats sold
(10+x)(100-2.5x)=1360
x=6
10+x=\$16
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A certain theater has 100 balcony seats. For every \$2  [#permalink]

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21 Jan 2016, 05:09
Suppose the price of a balcony seat = \$x
So, seats sold = 100 - [(x-10)/2]*5

But x*{100 - [(x-10)/2]*5} = 1360
-> x*{100 - (x/2 - 5)*5} = 1360
-> x*{100 - 5x/2 + 25} = 1360
-> x*{125 - 5x/2} = 1360
-> 125x - 5*x^2/2 = 1360
-> 250x - 5*x^2 = 2720
-> 50x - *x^2 = 544
-> x^2 - 50x + 544 = 0
-> x^2 - 34x - 16x + 544 = 0
-> x(x - 34) - 16(x - 34) = 0
-> (x - 34)(x - 16) = 0

So, x could be 34 or 16

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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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31 Mar 2017, 19:23
Hi Guys,

If found a different way to find the value. What do you think???

We can se that 1360=P*Q

then P and Q MUST be a factor of 1360

---Factors of 1360 = 2x2x2x2x5x17..... thus, P can [b]ONLY have as factors 2, 5 and 17[/b]

If you see the answers we have:

A. \$12 <-- has factor 3 WRONG
B. \$14 <-- has factor 7 WRONG
C. \$16
D. \$17
E. \$18 <-- has two times the factor 3 and we can hace onlye one at most WRONG

Now that we only have 2 answers we can "plug" the remainin factors of 1360 for each answers
C. \$16 =2x2x2x2<-- Q= 5x17 = 85
D. \$17 =17<-- Q= 2x2x2x2x5 =16x5>100 NOT POSSIBLE WRONG
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Re: A certain theater has 100 balcony seats. For every \$2  [#permalink]

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07 Dec 2018, 22:19
boomtangboy wrote:
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?

1360 = (10+2x)*(100-5x)
10x^2 - 150x +360 = 0
x=12,3

Therefore: 10+2*3 = 16
Re: A certain theater has 100 balcony seats. For every \$2   [#permalink] 07 Dec 2018, 22:19
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