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A movie theater regularly sells adult tickets for $12 and child ticket [#permalink]

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30 Jun 2011, 04:44

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43% (03:07) wrong based on 101 sessions

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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?

Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink]

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30 Jun 2011, 05:24

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

Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink]

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01 Jul 2011, 03:32

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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]

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01 Jul 2011, 04:34

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

Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink]

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05 Jul 2011, 05:21

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]

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17 Jul 2015, 09:13

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A movie theater regularly sells adult tickets for $12 and child ticket [#permalink]

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21 Dec 2015, 04:26

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)

Re: A movie theater regularly sells adult tickets for $12 and child ticket [#permalink]

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12 Mar 2017, 16:05

we can ballpark answers: lets start with B or D to estimate answers a 10% discount for children's tickets means for every ticket we receive 60 cents of savings and remaining 5% gives us +60 cents for each Adult's ticket Together 0.6*3 + 0.6*8 = $1.80 + $4.80 = $6.60 too much

let's try a 10% for Adult's ticket 3*$1.20 + 8*$0.30 = $3.60 + $2.40 = $6.00