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At a certain symphonic concert, tickets for the orchestra

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At a certain symphonic concert, tickets for the orchestra

by Mike@Magoosh » Tue Oct 22, 2013 10:36 am
At a certain symphonic concert, tickets for the orchestra level were $50 and tickets for the balcony level were $30. These two ticket types were the only source of revenue for this concert. If R% of the revenue for the concert was from the sale of balcony tickets, and B% of the tickets sold were balcony tickets, then which of the following expresses B in terms of R?
(A) 200R/(500 + 3R)
(B) 300R/(500 - 2R)
(C) 300R/(200 + 5R)
(D) 500R/(300 + 2R)
(E) 500R/(200 + 3R)

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by theCodeToGMAT » Tue Oct 22, 2013 8:17 pm
Thanks Mike!!

[spoiler]{D}[/spoiler]
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by vipulgoyal » Tue Oct 22, 2013 9:02 pm
eq becomes B*R/ (100-B)50 + B*30 = R/100
hence OA D[/spoiler]
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by sanju09 » Tue Oct 22, 2013 11:01 pm
Mike@Magoosh wrote:At a certain symphonic concert, tickets for the orchestra level were $50 and tickets for the balcony level were $30. These two ticket types were the only source of revenue for this concert. If R% of the revenue for the concert was from the sale of balcony tickets, and B% of the tickets sold were balcony tickets, then which of the following expresses B in terms of R?
(A) 200R/(500 + 3R)
(B) 300R/(500 - 2R)
(C) 300R/(200 + 5R)
(D) 500R/(300 + 2R)
(E) 500R/(200 + 3R)

For more practice problems involving percents, some tips about handling percent problems on the GMAT, and the OA & complete explanation of this particular problem, see:
https://magoosh.com/gmat/2013/gmat-quant ... h-percents

Mike :-)
Nice question Mike!

If a total of 100 tickets were sold, then B were balcony and 100 - B were orchestra. This would get a total revenue of $[30 B + 50 (100 - B)] = $(5000 - 20 B). Since, R% of the revenue for the concert was from the sale of balcony tickets, therefore we can have

$30 B = R% of $(5000 - 20 B)

Or (5000 - 20 B)/ (30 B) = 100/R

Or 500/ (3 B) = 100/R + 2/3

Or 500/B= (300 + 2 R)/R

Or B = [spoiler]500R/(300 + 2R)


Pick D[/spoiler]
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