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A movie theater regularly sells adult tickets for $12 and child ticket

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A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] New post 30 Jun 2011, 03:44
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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%
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Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] New post 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"
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Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] New post 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] New post 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] New post 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: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] New post 17 Jul 2015, 08:13
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Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink] New post 17 Jul 2015, 10:01
is there a short cut to solve this question besides plugging in values... just asking to explore methods...
Re: A movie theater regularly sells adult tickets for $12 and child ticket   [#permalink] 17 Jul 2015, 10:01
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