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# movie theater

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movie theater [#permalink]  30 Jun 2011, 03:44
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44% (01:10) correct 56% (01:25) wrong based on 9 sessions
A movie theater regularly sells adult tickets for $12 and child tickets for$6. On a certain day, the theater discounts these regular ticket prices at different rates so that a group of 3 adults and 8 children spends a total of $6 less than what it would regularly spend. If the sum of the two discount rates is 15%, what is the discount rate on each adult movie ticket? (A) 12% (B) 10% (C) 8% (D) 5% (E) 2% [Reveal] Spoiler: OA Math Forum Moderator Joined: 20 Dec 2010 Posts: 2035 Followers: 135 Kudos [?]: 1107 [0], given: 376 Re: movie theater [#permalink] 30 Jun 2011, 04:24 vinayreguri wrote: A movie theater regularly sells adult tickets for$12 and child tickets for $6. On a certain day, the theater discounts these regular ticket prices at different rates so that a group of 3 adults and 8 children spends a total of$6 less than what it would regularly spend. If the sum of the two discount rates is 15%, what is the discount rate on each adult movie ticket?

(A) 12%
(B) 10%
(C) 8%
(D) 5%
(E) 2%

Let the discount offered on adult tickets be x
Let the discount offered on child tickets be y

sum of the two discount rates is 15%
x+y=0.15
y=0.15-x ---------------------1

On a regular day, 3 adults would pay
3*12=36
But, with a discount of x, adults would have to pay 36x less
Likewise, with discounts, 8 children would have to pay 8*6y=48y less

3 adults and 8 children spends a total of $6 less 36x+48y=6 Divide by 6 6x+8y=1-------------------------2 Substituting the value of y from 1 in 2: 6x+8(0.15-x)=1 6x+1.2-8x=1 -2x=-0.2 x=0.2/2=1/10=0.1=10% Ans: "B" _________________ Intern Joined: 29 Jun 2011 Posts: 13 Location: Ireland Followers: 1 Kudos [?]: 5 [0], given: 0 Re: movie theater [#permalink] 01 Jul 2011, 02:32 The group of 3 adults and 8 children would usually spend$84 [3(12)+8(6)=84]. With the discounts they now spend $78. To translate this into an equation we use A as the discount on adult prices and C as the discount on children prices. We now have this equation: 3(12-A)+8(6-C)=78. The second bit of information we are told is that the sum of both discount rates is 15%. The adult discount rate is (100*A/12) and the childrens' rate is (100*C/6). So we have (100*A/12)+(100*C/6)=15. Now we have two equations to solve for A and C: 36-3A+48-8C=78 => 3A+8C=6 (multiplying out) (A+2C)/12=0.15 => A+2C=1.8 (finding a common denominator and dividing across by 100) Solving these simultaneously, we get: 2C=0.6 => C=0.3. Therefore the children discount rate is 100*0.3/6=5%. Since we know the combined rates are 15%, the adult discount rate is 10% and the answer is B. _________________ www.testprepdublin.com For the best GMAT, GRE, and SAT preparation. Manager Joined: 21 May 2011 Posts: 241 Followers: 0 Kudos [?]: 105 [0], given: 8 Re: movie theater [#permalink] 01 Jul 2011, 03:34 Since I know the total discount value is$6.
I would simply write down, 3.12.a/100 + 8.6.c/100 = 6
other equation given to us is a/100 + c/100 = 15/100

simplifying and solving for a we get 10%

B is correct
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Re: movie theater [#permalink]  05 Jul 2011, 04:21
vinayreguri wrote:
A movie theater regularly sells adult tickets for $12 and child tickets for$6. On a certain day, the theater discounts these regular ticket prices at different rates so that a group of 3 adults and 8 children spends a total of \$6 less than what it would regularly spend. If the sum of the two discount rates is 15%, what is the discount rate on each adult movie ticket?

(A) 12%
(B) 10%
(C) 8%
(D) 5%
(E) 2%

B for me

3*12*x%+8*6*(15-x)%=6
by solving this we get x=10%

hope this helps
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Re: movie theater   [#permalink] 05 Jul 2011, 04:21
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