percent

[venmic]

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% correct

(C) 8% your answer

(D) 5%

(E) 2%

please explain

[bubbliiiiiiii]

let discount on adult ticket be a and child ticket be b.

we know a+b =15 ..... I

From question,

3[12-(a/100)(12)] + 8[6-(c/100)(6)] = 78 .... II {78 = (3*12 + 8*6)-6}

By Solving I and II, we get a =10 and c=5.

[aplavakarthik]

The total cost for 3Adult tickets and 8 Child tickets is $84.

Discount given 15% which brings discount $6 =x%(36)+ (15-x)%48

So cost of total tickets is $78.

Plug in values for x

First option C - 8%

8%(36)+7%(48)
=2.88 + 3.24 -------which is more than 6.

Now to check B or D is the point.

The more % of discount u give to child tickets u get more discount. Here i have given 7 and got total discount more than $6.

So the discount i give to child tickets shd be less. Gmat arranges options in ascending or descending fashion.

So now check option B
10%(36)+5%(48)
=3.6 +2.4 =$6

Therefore B is the right answer.

[gmatboost]

$6 =x%(36)+ (15-x)%48

Why not just solve this equation once you have it?

$6 =x%(36)+ (15-x)%48

6 = .36x + 15*.48 -.48x

Shortcut: 10*0.48 is 4.8, so 15*0.48 is 4.8 + 2.4 = 7.2

6 = 7.2 -.12x
-1.2 = -.12x
1.2 = .12x
120 = 12x
x = 10