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

Question

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%

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

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Kinshook · Accepted Answer

Given: 
1. A movie theater regularly sells adult tickets for $12 and child tickets for $6. 
2. 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.

Asked: If the sum of the two discount rates is 15%, what is the discount rate on each adult movie ticket?

Let the discount rate on adult movie ticket be x%
The discount rate on child ticket will be (15 - x)%

Total discount of 3 adults and 8 children tickets = 3*12*x + 6*8*(15%-x) = 6
6x + 8(15%-x) = 1
6x + 1.2 - 8x = 1
2x = .2
x = .2/2 = 10%

IMO B

ShankSouljaBoi · Answer

B
Let D1 be discount percentage for adults and D2 be discount percentage for children.

We know that D1% + D2% = 15%
And

3*(1- D1%)*12 + 8*(1- D2%)*6 = 7800%
Solve for D1 = 10

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nick1816 · Answer

Let there is x% discount on Adult tickets, and y% on child tickets

(12*3)*{x/100}+(6*8)(y/100)=6.......(1)

Also, x+y=15......(2)

From (1) and (2), we get 
x=10
and y=5

kpstudies · Answer

I'm a little confused here. Question says that the discounted rate would be $6 dollars less than what they normally spend, so wouldnt the first equation be 3*12*x + 6*8*(15%-x) = 78? 78 is 6 less than the normal price for all of the tickets of $84

Thekingmaker · Answer

lenghty just solve the equations 6+ 12(1-0.0x)3 + 6(1-0.0y)8 =84 and 0.0x + 0.0y =0.15 and solve for X and we get 10 
 IMO B

ThatDudeKnows · Answer

We can also just Plug In The Answers (PITA).
I like trying B and D and those look like the easiest to work with, so we are in good shape.

3 adults at $12 each + 8 children at $6 each costs $36 + $48 = $84 regularly.

B: 3 adults at $10.80 each + 8 children at $5.70 each costs $32.40 + $45.60 = $78.
Is that what we wanted? Yep.

Answer choice B.

ThatDudeKnowsPITA

sayan640 · Answer

Let x be the discount on adult ticket and y be the discount on child ticket .
x+y=15....................(i)

3*12 (1- x/100) + 8*6 * (1 - y/100) = 36 + 48 - 6

36x + 48y = 600 ............................(ii)

36x + 36y = 540
SOlving ,

x=10
and y=5

Hence the discount on the adult ticket = 10

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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

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