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A certain theater has 100 balcony seats. For every $2 [#permalink]
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28 Apr 2012, 20:39
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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 I solved it as follows: 10+2(x) = 100 5(x) x= 12 Why is my approach wrong?
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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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30 Apr 2012, 02:53
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 = (10095) / (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, 06:54
The official answer given here is wrong, it is given E. Moderators please correct it, it'll be C.



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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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12 May 2012, 04:16
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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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.?



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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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12 May 2012, 10:56
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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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.? 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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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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31 May 2013, 05:22



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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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02 Jun 2013, 20:49
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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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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02 Jun 2013, 20:56
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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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.[/quote] 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, 20:46
(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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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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16 Oct 2014, 04:42
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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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+$2*x)(1005x)=1,360 where y is the number of tickets sold @10$



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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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16 Oct 2014, 06:51
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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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+$2*x)(1005x)=1,360 where y is the number of tickets sold @10$ 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, 09:46
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)(1005x)=1,360, where x is the # of times we increased the price by $2. (10+$2*x)(1005x)=1,360 > (5+x)(20x)=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+$2*x)(1005x)=1,360 where y is the number of tickets sold @10$ 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, 22:15
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 $2 [#permalink]
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09 Dec 2015, 19:14
solved it as everyone else: 1360=1000+150x10x^2 or (x3)(x12)
now, either x is 3 or 12. if 12, then the price would be 12*2+10 => 34$. 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, 14:37
let 10+x=seat price 1002.5x=number of seats sold (10+x)(1002.5x)=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, 04:09
Suppose the price of a balcony seat = $x So, seats sold = 100  [(x10)/2]*5
But x*{100  [(x10)/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
Since 16 is given in the answer choices, answer = C



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Re: A certain theater has 100 balcony seats. For every $2 [#permalink]
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31 Mar 2017, 18:23
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




Re: A certain theater has 100 balcony seats. For every $2
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