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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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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 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.

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.

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.?

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.?

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.

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

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.

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

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.

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+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$

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+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$

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. _________________

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.

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+$2*x)(100-5x)=1,360 where y is the number of tickets sold @10$

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]

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 _________________

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.

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