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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~fluke

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