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An auction house charges a commission of 15% on the first

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An auction house charges a commission of 15% on the first [#permalink] New post 28 May 2012, 19:37
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85% (02:23) correct 14% (01:29) wrong based on 5 sessions
An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?

A. $115,000
B. $160,000
C. $215,000
D. $240,000
E. $365,000
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 May 2012, 00:22, edited 2 times in total.
Edited the question and added the OA
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 29 May 2012, 00:28
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Smita04 wrote:
An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?

A. $115,000
B. $160,000
C. $215,000
D. $240,000
E. $365,000


Say the price of the house was $x, then 0.15*50,000+0.1*(x-50,000)=24,000 --> x=$215,000 (15% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).

Answer: C.
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 06 Sep 2012, 19:54
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carcass wrote:
Bunuel I would ask one thing if I can: in this kind of problem algebra (set up an equation) is faster than for instance backsolving in general, or always depends on you ??

Thanks


It Always depends on you!

For this question i did in this way.

50000 - 10 % = 7500
Then commission for remaining amount will be 24000-7500=16500

Then amount which gives this 16500 as 10% should be 165000.


Therefore summing up 165000+50000 = 215000

This was the way i felt easy for me. :-D
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Re: An auction house charges a commission of 15% on the first [#permalink] New post 06 Sep 2012, 18:37
Bunuel I would ask one thing if I can: in this kind of problem algebra (set up an equation) is faster than for instance backsolving in general, or always depends on you ??

Thanks
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Re: An auction house charges a commission of 15% on the first   [#permalink] 06 Sep 2012, 18:37
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