Problem Solving

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%

Answer is C?

Let us assume production costs are $10 a seat for the show. Choose an easy number to work with, such as 100 seats. So total production costs equal $1000. To get the 20% margin, tickets must be sold at $12/seat to earn $1200.

Now, it states that they actually sold only 95% of n (which in our case is 100), so 95*$12 (selling price)=$1140. Selling 95 tickets at $12/ticket earns $1140, which is $140 greater than production costs of $1000 or a 14% margin.

That's kind of a long way to figuring this out, but at least the math is easy to calculate. Someone else have an equation to use???

envyk10 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%

Let t be the ticket price and p be the cost of production

nt = 1.2p -- given

We are asked to find (0.95n)*t - p
= 0.95*1.2*p - p
= 1.14p - p
= .14p

So, this is 14% greater than prod cost

Hence C

set up a ratio

1.2p/1(n) = z/.95n

z=1.140

or 14%

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%

Cost of 100 tickets = $100
Each ticket for $1
Selling price = $120; each one for $1.2

Sold -- 95 @ 1.2 = 114
profit % = (114-100)/100 * 100 = 14%