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avg and ration question. how to solve?

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by tj123 » Sun Jul 12, 2009 3:57 pm
At a certain theater, the cost of each adult's ticket is $5 and the cost of each childs ticket is $2. what was the avg arithmetic mean cost of all the adults and childrens tickets sold at the theater yesterday?

1) yesterday the ratio of the number of children's tickets sold to the number of adult's ticket sold at the theater was 3to 2/

2) yesterday 80 adults tickets were sold at the theater

OA A
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Source: — Data Sufficiency |
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by mehravikas » Sun Jul 12, 2009 5:15 pm
IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
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by vittalgmat » Sun Jul 12, 2009 9:48 pm
Here is another approach.

Assume that a adults and c children tickets were sold.
The Question can be modified as follows
(5a +2c)/(a+c) = ?

stmt says c/a = 3/2
ie c = 3a/2 ----------(1)

substitute this ie the question.
(5a + 3a)/(a +3a/2)
simplifying,
16a/5a = 16/5 .. a definite answer
So sufficient.

Stmt 2 is not sufficient.

hence A
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by Musicolo » Mon Jul 13, 2009 2:15 am
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is? :)

Thanks a lot
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by hk » Mon Jul 13, 2009 10:09 am
Musicolo wrote:
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is? :)

Thanks a lot
The question is asking for the average cost of a ticket. In other words,

Answer = Total cost of all the tickets (cost of all adult tickets + total cost of all children's ticket) / Total number of tickets sold.

But St.1 alone is enough to calculate this answer since the ratio is given. In other words, 3/2 tells us that if 5 tickets were sold in total 3 were children's tickets and 2 were adults tickets. You can put this into the formula (above) and get the average price..
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by mehravikas » Mon Jul 13, 2009 5:40 pm
Hey Musicolo,

'hk" has given a nice explanation, I hope "hk" has cleared your doubt?
Musicolo wrote:
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is? :)

Thanks a lot
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by Musicolo » Mon Jul 13, 2009 11:16 pm
hk wrote:
Musicolo wrote:
mehravikas wrote:IMO - A

Children tickets = 3x, adults = 2x

Mean = 5 * 2x + 2 * 3x / 3x + 2x = 16/5
Hi, Thanks for your explanation. Its very clear and concise but could you please explain to me what is this 16/5 now? what does it represent?

I am not clear as to what the question is? :)

Thanks a lot
The question is asking for the average cost of a ticket. In other words,

Answer = Total cost of all the tickets (cost of all adult tickets + total cost of all children's ticket) / Total number of tickets sold.

But St.1 alone is enough to calculate this answer since the ratio is given. In other words, 3/2 tells us that if 5 tickets were sold in total 3 were children's tickets and 2 were adults tickets. You can put this into the formula (above) and get the average price..
Thanks :)
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