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Total Tickets Sold in a theather

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Total Tickets Sold in a theather

by nusa84 » Fri Jul 16, 2010 8:39 am
Hi,

I can't get the exact number, perhaps I am reasoning it wrong, any ideas? thanks!

On a certain day, a theater sold 30 tickets every 5 minutes, from 9:00 A.M. to 5:55 P.M., inclusive. Regular tickets are worth $10, and discount tickets are worth $6 each. If the regular tickets sold were four times as many as the discount tickets sold, what was the total revenue, in dollars, on that day?

A. 19,442
B. 22,350
C. 24,720
D. 29,532
E. 32,470

OA: D
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by kvcpk » Fri Jul 16, 2010 8:56 am
nusa84 wrote:Hi,

I can't get the exact number, perhaps I am reasoning it wrong, any ideas? thanks!

On a certain day, a theater sold 30 tickets every 5 minutes, from 9:00 A.M. to 5:55 P.M., inclusive. Regular tickets are worth $10, and discount tickets are worth $6 each. If the regular tickets sold were four times as many as the discount tickets sold, what was the total revenue, in dollars, on that day?

A. 19,442
B. 22,350
C. 24,720
D. 29,532
E. 32,470

OA: D
R and D be the regular and discounted ticket counts
R=4D

30 tickets every 5 mins emans 12*30 tickets per hour.
There are 9 hours - 5mins
So 108*30 - 1*30 = 107*30 tickets were sold.

R +D =107*30
5D = 107*30
D = 642
R = 2568

Revenue from R = 2568 * 10 = 25680
Revenue from D = 642*6 = 3852
Sum = 29532

Hope this helps!!
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by GMATGuruNY » Fri Jul 16, 2010 9:01 am
Here's an efficient way to determine the correct answer:

For every 4 regular sold, 1 discount is sold.
Revenue regular = 4 * 10 = 40.
Revenue discount = 1 * 6 = 6.
Revenue ratio = 40/6 = 20/3, so revenue from regular is 20/23 of total.
Need an answer divisible by 23.
Only D works: 29532/23 = 1284.

The correct answer is D.
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by nusa84 » Fri Jul 16, 2010 9:07 am
Very clear! Thank you for your explanations! I probably got the calculation wrong.
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by hero » Fri Jul 16, 2010 11:01 am
kvcpk wrote:
nusa84 wrote:Hi,

I can't get the exact number, perhaps I am reasoning it wrong, any ideas? thanks!

On a certain day, a theater sold 30 tickets every 5 minutes, from 9:00 A.M. to 5:55 P.M., inclusive. Regular tickets are worth $10, and discount tickets are worth $6 each. If the regular tickets sold were four times as many as the discount tickets sold, what was the total revenue, in dollars, on that day?

A. 19,442
B. 22,350
C. 24,720
D. 29,532
E. 32,470

OA: D
R and D be the regular and discounted ticket counts
R=4D

30 tickets every 5 mins emans 12*30 tickets per hour.
There are 9 hours - 5mins
So 108*30 - 1*30 = 107*30 tickets were sold.

R +D =107*30
5D = 107*30
D = 642
R = 2568

Revenue from R = 2568 * 10 = 25680
Revenue from D = 642*6 = 3852
Sum = 29532

Hope this helps!!
wait...if r=4d, then from R+D, how do you get 5D? wouldn't that be 8D or 5R? am i missing something? all the calculations work though if you divide by 5, i just don't see the 5D.
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by GMATGuruNY » Fri Jul 16, 2010 11:57 am
hero wrote:
kvcpk wrote:
nusa84 wrote:Hi,

I can't get the exact number, perhaps I am reasoning it wrong, any ideas? thanks!

On a certain day, a theater sold 30 tickets every 5 minutes, from 9:00 A.M. to 5:55 P.M., inclusive. Regular tickets are worth $10, and discount tickets are worth $6 each. If the regular tickets sold were four times as many as the discount tickets sold, what was the total revenue, in dollars, on that day?

A. 19,442
B. 22,350
C. 24,720
D. 29,532
E. 32,470

OA: D
R and D be the regular and discounted ticket counts
R=4D

30 tickets every 5 mins emans 12*30 tickets per hour.
There are 9 hours - 5mins
So 108*30 - 1*30 = 107*30 tickets were sold.

R +D =107*30
5D = 107*30
D = 642
R = 2568

Revenue from R = 2568 * 10 = 25680
Revenue from D = 642*6 = 3852
Sum = 29532

Hope this helps!!
wait...if r=4d, then from R+D, how do you get 5D? wouldn't that be 8D or 5R? am i missing something? all the calculations work though if you divide by 5, i just don't see the 5D.
R + D = 107*30
Substitute 4D for R (since 4D = R)
4D + D = 107*30
5D = 107*30.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
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by hero » Fri Jul 16, 2010 1:12 pm
GMATGuruNY wrote:
hero wrote:
kvcpk wrote:
nusa84 wrote:Hi,

I can't get the exact number, perhaps I am reasoning it wrong, any ideas? thanks!

On a certain day, a theater sold 30 tickets every 5 minutes, from 9:00 A.M. to 5:55 P.M., inclusive. Regular tickets are worth $10, and discount tickets are worth $6 each. If the regular tickets sold were four times as many as the discount tickets sold, what was the total revenue, in dollars, on that day?

A. 19,442
B. 22,350
C. 24,720
D. 29,532
E. 32,470

OA: D
R and D be the regular and discounted ticket counts
R=4D

30 tickets every 5 mins emans 12*30 tickets per hour.
There are 9 hours - 5mins
So 108*30 - 1*30 = 107*30 tickets were sold.

R +D =107*30
5D = 107*30
D = 642
R = 2568

Revenue from R = 2568 * 10 = 25680
Revenue from D = 642*6 = 3852
Sum = 29532

Hope this helps!!
wait...if r=4d, then from R+D, how do you get 5D? wouldn't that be 8D or 5R? am i missing something? all the calculations work though if you divide by 5, i just don't see the 5D.
R + D = 107*30
Substitute 4D for R (since 4D = R)
4D + D = 107*30
5D = 107*30.
stupid mistake on my part. 1 quick re-write and everything makes sense. thanks for the explanation. i need to get some sleep.
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