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Word Problem

by heshamelaziry » Fri Dec 04, 2009 12:01 pm
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%

OA C

Could you guys say what is the level of this question ?
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by ace_gre » Fri Dec 04, 2009 12:35 pm
number of tickets =n
The key here is that Production cost(P) does not vary with n. Only revenue(R) varies with n

R=1.2 P
say n=100, cost of 1 ticket =1
then for n tickets R=100
P=100/1.2

Now n-->95, R=95
Required %= ((R-P)/P)*100
==>(95-100/1.2)/(100/1.2) =14
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by heshamelaziry » Fri Dec 04, 2009 12:45 pm
Is this correct ?

Say the production cost is $100 for 20 tickets. The revenue is 1.2 the production cost = $120 -----> each ticket price is $6

if 95% if the tickets sold, then 19 tickets were sold for 19 * 6 = $114

So, (114 - 100)/100 * 100= 14
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by ace_gre » Fri Dec 04, 2009 1:00 pm
I do not see why not..and it looks simpler and easier!!!
:D
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by ssuarezo » Mon Dec 07, 2009 10:57 am
Hi:
Another way: Since price is constant: Rule of 3:

If n makes 1.20
then 0.95n makes x
--> x = (1.20*0.95n)/n --> x=1.14, that is, 14%

Silvia
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