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# If an organization were to sell n tickets for a theater production, th

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Math Expert
Joined: 02 Sep 2009
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If an organization were to sell n tickets for a theater production, th [#permalink]

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02 Apr 2017, 21:51
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Question Stats:

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If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?

(A) 4%
(B) 10%
(C) 14%
(D) 15%
(E) 18%
[Reveal] Spoiler: OA

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Re: If an organization were to sell n tickets for a theater production, th [#permalink]

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03 Apr 2017, 06:54
Let n = 100; Price of each ticket = 12
Cost = (Revenue)/1.2 = (100*12)/1.2 = 1000

Suppose the organization sold all but 5% of tickets i.e. 95 tickets, then revenue = 95*12

Percentage required = ((95*12 - 1000)/1000)*100 = (1140 - 1000)/10 = 14%

Intern
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Re: If an organization were to sell n tickets for a theater production, th [#permalink]

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03 Apr 2017, 07:59
revenue for n tickets = 1.2*(total costs of production), take total costs = c
asking what is the revenue for 0.95n tickets ?
I reasoned it as: for n tickets-> 1.2c, then for 0.95n tickets-> what c? taking the cross-multiplication we get = 1.2*0.95 = 1.14c, it means revenue is 14% greater than production costs.
Manager
Joined: 14 Sep 2016
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Concentration: Finance, Economics
If an organization were to sell n tickets for a theater production, th [#permalink]

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03 Apr 2017, 09:51
Bunuel wrote:
If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?

(A) 4%
(B) 10%
(C) 14%
(D) 15%
(E) 18%

Pick numbers.
N= 20
Cost = $100 Revenue +20% =$120

Results of numbers picked.
Unit price of N = \$6
N - 5% = 19 tickets
New revenue = 19 * 6 =114
Cost 100, new revenue 114, increase 14%
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Re: If an organization were to sell n tickets for a theater production, th [#permalink]

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29 Jun 2017, 21:14
Simple ratio problem here.

100/120 = 95/x. x = 114, or 14% greater than cost.
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Re: If an organization were to sell n tickets for a theater production, th [#permalink]

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29 Jun 2017, 21:45
$$n = 1.2p$$
$$0.95n = xp$$

$$x = \frac{0.95n * 1.2p}{pn} = 0.95 * 1.2 = 1.14 = 14%$$. Ans - C.
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Re: If an organization were to sell n tickets for a theater production, th [#permalink]

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12 Apr 2018, 16:26
Bunuel wrote:
If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?

(A) 4%
(B) 10%
(C) 14%
(D) 15%
(E) 18%

If we let c = the total cost of production, then 1.2c = the revenue from selling n tickets. Another way of saying this is that selling n tickets results in 1.2c. But we want to determine the total revenue from selling 95% of the tickets, or 0.95n. If we let x = the total revenue from selling 95% of the tickets, we can create the proportion:

n/1.2c = 0.95n/x

nx = (1.2c)(0.95n)

nx = 1.14nc

x = 1.14c

The total revenue from selling 95% of the tickets is 1.14c, which means that the total revenue is 14% greater than the cost of production.

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Re: If an organization were to sell n tickets for a theater production, th   [#permalink] 12 Apr 2018, 16:26
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