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

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Bunuel
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If an organization were to sell n tickets for a theater production, th [#permalink] New post   02 Apr 2017, 21:51
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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%
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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   12 Apr 2018, 16:26
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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.

Answer: C
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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   03 Apr 2017, 06:54
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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%

Answer: C
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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   03 Apr 2017, 07:59
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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.
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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   03 Apr 2017, 09:51
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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] New post   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] New post   29 Jun 2017, 21:45
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\(n = 1.2p\)
\(0.95n = xp\)

\(x = \frac{0.95n * 1.2p}{pn} = 0.95 * 1.2 = 1.14 = 14%\). Ans - C.
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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   26 Dec 2018, 04:34
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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%

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Toal numbet of tickets = 100
Cost per ticket = 1 EUR
Total cost = 100 EUR
Selling price = 1.2 EUR
Total revenu = 120

BUT
Sold 95 Tickets
Total revenue 95*1.2 = 114

so, \(\frac{(114-100)}{100} *100% = 14\)
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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   17 May 2021, 08:55
You can use a simple proportion equation.


Quantity or tickets sold is directly proportional the “percent greater” than the Total Costs

Let C = Total Costs

100% * (N) ———————> 120% * (C)


95% * (N) ———————> (P %) * (C)


120% (C) * (95% / 100%) = P%

1.2 * .95 = 1.14 ———-> or 114% of Total Costs

Which is 14% greater

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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   06 Jan 2023, 09:53
Let,
Total cost= 100
Hence, revenue is 120

Let, the price of ticket is $1
Hence ticket sold is 120

If, 5% ticket is unsold, then the number of ticket sold is 114. Hence revenue is 14. Which is 14%. 🙂

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Re: If an organization were to sell n tickets for a theater production, th [#permalink] New post   31 Jan 2024, 09:39
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