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A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] ### Show Tags 30 Jun 2011, 03:44 6 This post was BOOKMARKED 00:00 Difficulty: 75% (hard) Question Stats: 57% (04:26) correct 43% (03:07) wrong based on 81 sessions ### HideShow timer Statistics 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
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Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] ### Show Tags 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: 3 Kudos [?]: 7 [2] , given: 0 Re: A movie theater regularly sells adult tickets for$12 and child ticket [#permalink]

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01 Jul 2011, 02:32
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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.
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Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] ### Show Tags 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: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] ### Show Tags 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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17 Jul 2015, 10:01
is there a short cut to solve this question besides plugging in values... just asking to explore methods...
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21 Dec 2015, 03:26
Back solving is easier and faster for this problem.

We know that the sum should be 15%
First we calculate the total without discount.
Adult = 12 * 3 = 36
Children = 6*8 = 48

For back solving, in particularly this one I start on D, because its an easy number:(Normally I would choose C)
D) (36*0,05) + (48*0,1) = 4,2 (too low, so the adult ticket received a bigger discount, lets try B that is also an easy number)
B) (36*0,1) + (48*0,05) = 6 (Correct)
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23 Oct 2016, 08:32
backsolving helps to solve this problem quickly.
Although I am more comfortable with algebra.
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